That's the joys of open systems A standard was never established, that's all - or better: Too many standards were introduced, but not enforced (which is impossible anyway).
One big obstacle was the Steam platform, which denied any standard Microsoft had introduced.

On open system like Windows or Linux there are so many vendors, each one with it's own agenda (I'll talk about Windows here, but many points are also valid for Linux)

What doesn't make it easy, is the separation between PC user and Shop user.
On a PC there can be multiple PC users.
Those are customers of multiple shopsm can have more than one account in each shop.
On the other hands these multiple PC users can share shop accounts.
Try to bring a system into that

Microsoft tried, but ultimately failed. Of course their approach was, that the PC user was the master account.

In the old days (DOS), there was no structure. Profilles and saves were often placed in the game directory itself. This was done until Windows 7 came along. Then it became a problem, because MS started to lock access for the program files folder for non-admins. This is the reason why many games from that time require admin rights to run.
If you install them in a directory without access restrictions, you won't need admin rights.

Some games would save their data somewhere in the userprofile, others would use the common user.

Microsoft had good intentions by introducing "%userprofile%\Saved Games", but hardly anyone used it.
Another version of it was available for the public user, but that confused both users and programmers.

Then we had of course Steam coming along with half baked cloud synchronization which would only work in the directory that was created for Steam user profiles ... bad idea when it comes to get some order into the whole thing.

With the introduction of user rights, Microsoft defined

A common path is
%userprofile%\Documents\Companyname\GameTitle
or - even worse:
%userprofile%\Documents\GameTitle
But I don't really like that. Documents is supposed to be for documents. But so many devs use this, that it's hard to get back from it.
I created a _docs directory in my documents directory, so my own documents would not get mixed up with savegames ...

I think the best idea would be either
%appdata%\<Companyname>\<Gametitle>\
or
%localappdata%\Companyname\Gametitle\
(localappdata is for data not to be synchronized, the other one will be synchronized for network users)

A modern standard for storing data is using the same structure that program classes have. That's also used on systems like Android.
%appdata%\com\company\gametitle\

Note that I use environment variables for user directories, which don't have necessarily to be on the system drive.
Now immagine that before Windows XP 64 Bit, the user directory was language dependent and many programmers too stupid to use the environment variables (sometimes they still are, but now they can't mess up that badly anymore).
So you could have hardcoded directories like
C:\Benutzer\SomeNorwegianNameWithSpecialCharsThatTheGameCan'tHandle\Dokumente
These days all Windows versions use english names and display language dependent names only as Alias.

The worst way ever of storing savegames I found in the PC version of the adventude called Hook.
The whole game was stored in one file called HOOK.EXE (~3MB)
When you saved a game, it would alter that .exe file and write the save game data directly into it ...

A honorable mention are also some Amiga games.
While it was common practice to use an extra disk for save games, some would write save data on one of the program disks which in the worst case would destroy the game for good (in the case of Hook on the PC you could just reinstall the game). That's why they didn't add copy protection to that disk and players could make a copy in order to play. Of course not everyone did that.