Thank you for your help. It is an issue not just on steamdeck, but on linux overall. I did some experimenting and figured out that the last properly working version of openal32.dll for thief1&2 is 1.22.2 released on June 27, 2022. I think there were some big changes (like routers) in 1.23 that broke something in thief games. Also, you can still use hrtf on pre 1.23 dlls and I recommend doing so.

TLDR:
- Download openal-soft-1.22.2-bin.zip from here or here and extract it somewhere.
- Rename bin/win32/soft_oal.dll to OpenAL32.dll and copy it into the thief main folder.
- Create a new txt file in the thief main folder with this inside:
Code:

[General]
channels=stereo
resampler=cubic
stereo-mode=headphones
hrtf=true
frequency=48000

and save it as "alsoft.ini"
- Download the HRTF/3D audio profile (xxxx-4800.mhr) that sounds most positionally accurate to your ears and copy it to the thief main folder.
- Settings in game: audio channels - 48 ; Hardware Acceleration - OpenAL ; EAX Setting - on
- That's it, there is no need to install OpenAL system/prefix wide.

PS There is a lutris installer "thief-gold-gog-newdark" that uses OpenAL 1.23.1 but for some reason it moves soft_oal.dll into the folder of the same name instead directly into the game folder (I think it some bug/mistake in installer) which obviously doesn't work and then relies on default gog installer OpenAL 2.0.7.0(which sounds awful). Even when you fix it and move soft_oal.dll where it should be, you get back to zero with popping audio again...
TLDR: Don't use it.