The seemingly unsolvable problem:
Since last year I've been unable to initiate and run the installation of said GeForce drivers on my second rig running Win10.

The last, or one of the last WHQL drivers (downloaded from the NVIDIA website) that starts and brings up the setup wizard's interface guiding through the installation process is 511.23 (from January 2022), all subsequent releases up until now either just show the small green splash screen and then nothing or, in case of the most recent ones (like 536.99 from a month ago), immediately close the NVIDIA Install Application process (briefly visible in the task manager) after executing the corresponding setup.exe.

Which I only get access to by manually unpacking the .exe WHQL archive, by the way.
Every attempt at the standard automatic unpacking (which, by default extracts everything to C:\NVIDIA\DisplayDriver) results in the NVIDIA Install Application process being killed and the unpacked installation files deleted again.

The standard trouble-shooting I've been through already numerous times (Run as administrator, run in safe mode, run from another drive/partition other than C:\, temporarily disable anitivirus, etc) and I've always made sure that there's enough free space available for the unpacking and installation process to commence (which, as I said, it did up until and including 511.23) but it just refuses to even progress to thw setup wizard/installation dialog.

A bit of research brought up the event viewer and in particular the application log to possibly get to the bottom of as to why processes get shut down but there was no log entry for the NVIDIA Install Application process at the time stamp I tried to run it (and it immediately got killed again).

Having exhausted every possible solution (I'm tech-savvy enough and capable of at attempting) I thought it might be worth a shot asking around these parts, if somebody maybe has an idea how to solve this conundrum.

Thank you very much in advance.

Can you manually unpack the .exe WHQL archive and then update the driver from the Device Manager?

That very much sounds as if some AV software is blocking it.

What card are you using? Is it a PCI card or a integrated Laptop solution?
If you are using a laptop, try not using the drivers from the Nvidia site, but the ones provided by your manufacturer.

Be aware that Nvidia dumped the old driver model for good since December 2021 now and by now only releases DCH drivers (starting with January 2022, like in your problem description). If you have a "standard" (legacy) driver installed, that one must be removed first in order to install the DCH driver.
Just for fun: try to install the last standard driver from 2021, see if that works.

And last but not least: I know you gonna hate this, but ... have you tried letting Nvidia Experience update the driver?

Exactly what I've been doing since it won't install the old-fashioned way any longer.
Problem is, that in some games like Steelrising or most recently Baldur's Gate 3 things like DLSS either don't work properly or don't show up as a graphics option at all.

Which I assume is the result of the bare-bones drivers-only installation via the device manager. Things like the latest PhysX and updating RTX features like DLSS aren't part of that. Isn't antivirus deactivated by default in safe mode?
As I said, attempting a normal installation ends in the NVIDIA Install Application process being killed immediately and the temporary unpacked setup files being wiped again - no matter if it's in safe mode or in "normal" mode with antivirus manually disabled beforehand.

I'm going to give it another shot later, just to be absolutely sure. RTX 3070, on an "off-the-grid" version of Win10 that hasn't been updated since ca. 2020 and has a whole bunch of background services and processes set to either deactivated or "run manually" at the very least.

Which I initially thought could be culprit (some deactivated service or process required for the WHQL drivers installation routine to function properly) but then again the services and processes haven't been touched since 2020, by me nor by Windows.
And the WHQL drivers setup wizard from January 2022 (511.23) does work, so it can't be that?

Unless newer versions of the installation routine suddenly do require some service or process that's currently set to deactivated? The drivers from January 2022 (511.23) whose corresponding setup wizard runs just fine are DCH drivers:
511.23-desktop-win10-win11-64bit-international-dch-whql.exe Just like Galaxy - NOT an option.

Wouldn't know about safe mode, but check the AV log - just in case.

You might want to try teh NVidia forums, there's surely some tech guys who can tell you what log files to check.

And yes, a outdated Windwos can cause all sorts of problems, a lot of software relies on the user keeping his system up to date.

You might want to give a try to NVCleanstall from TechPowerUp.

This could be the cause. I also deactivate unnecessary services and at some point noticed exactly the same problem with a new nvidia driver. Make sure the following services are enabled before installing: clipsvc, AppXSvc, AppMgmt, camsvc, Appinfo, bfe, nsi, mpssvc.

It's a firm possibility. Given the fluid nature of Windows, driver testing and updating is done on updated machines and may need current versioning to interact with. I'm no expert though.

And you final sentence in the quote ... why not? nVidia's driver development doesn't have to be in lockstep with Microsoft's changes. It just might happen in the future, is all. So a newer-than-the-OS driver package may work, or it may not. It's all up to nVidia an/or Microsoft. Nothing is close to being guaranteed outside of a fully up-to-date / supported system.

The only thing I can think of left to try is to uninstall the old drivers before installing the new ones.

No mention of the setup.exe in the log. Might try that as last resort option. Just did a test run and let it build a custom installation package, which doesn't work either, unfortunately.
Since it also executes the setup.exe, and from there it's the exact same chain of events as if I would attempt the regular, unmodified installation, with setup.exe resp. the NVIDIA Install Application process briefly popping up in the task manager before being killed and the temporary unpacked installation files in C:\NVIDIA\DisplayDriver being wiped. Didn't work either, unfortunately, both in normal as well as safe mode.
Thanks for the suggestion though. Already tried that as well, to no avail. I get that, but at least for now I refuse to believe that a fully up-to-date OS (or biting the bullet and install GeForce Experience) is the only solution to this particular issue.

Something causes setup.exe resp. the NVIDIA Install Application process to close prematurely before the actual installation routine with the NVIDIA Installer interface can commence, I "just" need to figure out what that something is.

Anyone know of a tool or piece of software that can track and log an executable's calls on services, processes or other dependencies during its runtime?

Are you 100% sure that you started these services successfully before installation? Maybe you disabled other ones, so dependencies are not met. It's probably a good idea to reset all to their default values first.
Maybe the cause lies somewhere else, but since I also experienced the exact same symtoms as you with a 5xx driver last year, I'm pretty sure it's related.

Got it figured out, finally.
Here's what the issue was and how I solved it:

1. Downloaded Process Monitor (Viele Dank for the suggestion, Swedrami, much appreciated) and ran it
2. Had it filter by process name ("setup") and start a fresh Capture
3. Ran the NVIDIA drivers' setup.exe and stopped the Capture in Process Monitor
4. Went through all of the 18000 events that got logged during the >1 second runtime
5. Noticed quite a few failed certificate-related fetch attempts
6. Brought up setup.exe's properties and digital signatures section...
7. ...and there it was: an expired and therefore untrusted root CA certificate
8. Checked 511.23's digital signatures/certificates, which, as expected, were all in order, valid and trusted
9. Downloaded the missing certificate from the CA's official website
10. Installed it into the required folder ("Trusted Root Certification Authorities")

And that was it.

Just finished downloading the latest GeForce WHQL drivers from a week ago (537.42) and after the unpacking of the temporary installation files it progresses to the setup wizard just fine now.

Bitte schön, glad to hear you got it sorted out.