It seems the reason Steam achievements aren't working on the Deck is because applications running in Wine aren't aware of the whole Linux environment and thus doesn't see the Linux version of Steam. I figured out a solution by installing the Windows version of Steam to my wine prefix and using that to launch the game as a non steam game. Through that I was able to get the game to recognize Steam and run. It's not an elegant solution, but if you want achievements, here's some instructions on how I did it.
I first configured my wine prefix to say it is Windows 10. This is necessary because wine prefixes are set to Windows 7 by default and Steam can't run past 30 days in a Windows 7 or 8 environment.
To do this select your game in Lutris, click the wine glass at the bottom, and select Wine configuration. At the bottom of the window that opens, change the bottom drop menu to Windows 10, click apply, and close the window.
I next installed Steam by opening up winetricks again and selecting "install an application." In the new window, scroll down to steam, select it's box and hit OK.
Something will pop up in the background a few times talking about 32-bit 64-bit prefix compatibility, those can be ignored. You can close the windows related to winetricks now.
Now add Steam to Lutris like you did with SYW with the + in the top left. Make sure you have the wine runner selected and you set the wine prefix.
When adding your Steam Executable your path will look something like this "/home/deck/<path to prefix>/drive_c/Program Files (x86)/Steam/steam.exe" and then save this config.
I then just launch steam through Lutris and login. Now for me, some steam menus bug out but it's still usable. I go to the Games menu at the top left of steam and add a non-Steam game. Browse and select "/", "home", "deck", all the way up to where FF7.exe is located.
The final step is to add a Steam shortcut from Lutris into Steam for controller support in the desktop and to play FF7 from Gaming Mode.
Hopefully I didn't miss anything and this helps!
