Here is your lesson number two (perhaps you know it already, but judging by your response I assume you don't).
"Old" Linux ports (before Vulkan and then some) were on OpenGL... Which depending on version could arguably have worse visual quality than DX > Vulkan translated one.
Not to even mention many Linux ports perform worse natively than when running them DX > Vulkan style.
(some are even hacked together monstrosities - for example Deus Ex Mankind Divided port by Feral Interactive - it is running a literal Feral Interactive made DX > OpenGL wrapper and the performance and reliability of that is atrocious)
There are also things such as older libraries used for the Linux ports (which would result for example in worse audio quality, less input options, etc).

There is PLENTY of reasons to run DXVK windows versions instead of native Linux ports.
The native ports are often atrocious, and if not, they often just perform better under DXVK.
That's it.
There is plenty of people who run Hitman 2016 and Alien Isolation like that for performance reasons.

Btw I forgot one more resource for looking:
(reddit) /r/linux_gaming/

In regards to this game on wine...
Well... Considering it is now using Vulkan on windows afaik ( at least PCGW directly suggests that https://www.pcgamingwiki.com/wiki/The_Talos_Principle#API ) it may be a tough search.
So far I only found this
https://www.youtube.com/watch?v=HCmF4gZigzA
and based on that this was 4 years ago and combining it with my knowledge I would say that by now this game is very likely totally playable on wine.
As to how to configure it, I don't know, you would likely have to experiment (I suggest doing this on Lutris anyway) as to what dlls are needed (also I suggest using Wine Proton GE builds in Lutris instead of vanilla ones).

And yes, this indeed IS related to quality of wine reports too. Because if there exists a windows port for a game that has native linux port then there always shall be SOMEBODY in this world who would want to run it for whatever reason.
The problem we are facing in this and many such directly similar circumstances is same as with "fixes for obscure rare issues" of all kinds (in linux).
It's that people who know just don't report things.
Whether you like it or not and regardless of how we look at it it's a fact that rather small cut of all people doing some testing actually report results in ANY way.
People DEFINITELY DID run this game the way you want it to, but it's either close to nobody reported it or the reports are drastically hidden deep somewhere.
Same situation (tho less drastic) is for example with Portal games and Team Fortress 2. They have native ports, yes, and people tend to go all "why would you want to run it this way if it has native port blah blah yada yada", so there aren't too many reports for those either (but they are findable at least).

EDIT:
For the sake of clarity and completion.
Yes. I did see those:
https://www.protondb.com/app/257510
https://github.com/ValveSoftware/Proton/issues/2861
BUT this is almost definitely a case of somebody's (tester's) inability to configure it properly.
How I know it? Vague details and the kind of bug experienced can usually generally be overcome with enough digging ( not to even mention that the profile that posted that report has LITERALY this same EXACT report for 2 DIFFERENT GAMES https://www.protondb.com/users/1221197695 ).

( here is rather tasteful example what it means when people are incompetent and post "broken" for working games - https://www.protondb.com/app/502500 - people often check if it works out of the box, then give up and post "broken" report. Also since you probably don't know this game's particular case - some people say that controller "isn't working. PERIOD" - that is incorrect, it's just that those people are unable to get themselves to dig enough in publicly available resources to fix it themselves and thus they say instead that "it doesn't work. PERIOD")

I had been wanting to play this for years, and was happy I could finally give it a try a few weeks ago when it hit Game Pass during my free trial, but was disappointed when my trial ended because I was not able to finish the game and it was just starting to get very interesting, nor was I about to jump on Steam and buy it.

Croteam should have offered this game to GOG years ago. Day one buy (on here). All the extras are a great touch.

Yes!. This is why I buy games from gog, because of games like The Talos Principle. Thank you gog. We gripe about things that happen on gog but on the whole they do a pretty awesome job of bringing DRM-free games to us, and at bargain prices..

Wishlist entry for Linux:

https://www.gog.com/wishlist/games/talos_principle_linux_version

Time to fight for our Linux rights! No tux, no bucks!

Thanks, that is $1.39. I'll buy this game when the publisher and GOG match that price for my region.

As the prominent digital PC gaming store, it is their plan B in case Microsoft goes ahead to step by step lock Windows down to Microsoft Store, and even before that to put some pressure on Microsoft on the aforementioned issue.

So basically Valve tries to make sure they have somewhere else to go continue their PC gaming business in case Windows becomes too hostile to them due to MS actions.

I could be wrong of course, but I don't believe the reason for Valve investing so much on Linux gaming is because Valve believes they make so much more money with Linux support at this point.

And yes I am an avid Linux user. I still play mostly on Windows but I kinda wish Linux gaming would pick up too, then I would play there more (currently I mainly play Team Fortress 2 on Linux).

As for GOG, I presume their owners (shareholders) have more the mindset of "concentrate on what is bringing in money NOW!", rather than investing into various what-if scenarios. I guess Valve has more money for such endeavors.

I bought the GOG version even without Linux, but I will also support that wishlist entry.

Okay, classic ruckus, as usual.
I have a practical question: Has anyone tried this (DRM-Free) version under Wine (DXVK)?

Does the game allow the user to save at any time?

It has save points that will auto-save your progress as you move through them. It's pretty non-invasive, and works well.

Thanks for the info!

You bet! I haven't played it in years, but I've been enjoying being back in it the past few hours.

You may want to take a look at these:
https://www.gog.com/forum/the_talos_principle/does_the_windows_version_work_with_wine
https://www.gog.com/forum/the_talos_principle/linux_and_mac_os_versions/post14

So, need a little Piggly Wiggly and will be playable. Ok.

P.S. The second link is completely useless - it is not for those who want to play this game on Linux.

I don't mind paying full price for games that deserve it. This is a really good game and, when such a game comes to GOG (of course, much later than on Steam, we all know GOG is always an afterthought of most developers) I even go out of my way to wait for the discount to run off to buy. But, if they won't arse to release it fully with the Linux version, they are adding insult to injury, so the cheapest price it is. You don't care about us GOG users, I won't care about your bottom line.