I can confirm the same issue also on Arch Linux.

https://github.com/ValveSoftware/Proton/issues/4616

Hi @kisak-valve, i am having issues with Proton and this game. The Linux port is awful, so i tried tunning it via proton, only to find that the game boots, but there are no menus. It's only the background.
steam-362890.log
Line(s) of interest: 12905.961:00cc:00d0:warn:debugstr:OutputDebugStringA "Qt:Warning (Thread Id: 208): DirectWrite: CreateFontFaceFromHDC() failed (Unknown error 0x88985000.) for QFontDef(Family="", pointsize=8.5, pixelsize=11, styleHint=5, weight=50, stretch=100, hintingPreference=0) LOGFONT("MS Sans Serif", lfWidth=0, lfHeight=-11) dpi=96 (:0, )\n"

Menu fonts don't show up on any proton version, including GE, but they do on older version of the game - crossfire-update(cu2). You can select that one in Black Mesa - Properties - Betas.
Anyway, here's a log of the current version on 6.3-7.

Compatibility Report
Name of the game with compatibility issues: Black Mesa
Steam AppID of the game:362890

System Information

• GPU: nVidia
• Driver/LLVM version: nVidia-495 Ubuntu Launchpad PPA
• Distro version: kDE Neon 20.04 w/ Kwin X11 Compositor [ ON ]
• Kernel 5.13-23-23-generic Canonical Propsed PPA
• Link to full system information report as Gist: https://gist.github.com/username-murphy/cecc0bf365612034a71fc2ccc8aa1484
• Proton version: 6.3-8/ 101221- [NoLaunchOptions]
  Same as others.

• No Menu (s) -bluffed my way passed with random blind screen clicking .
• • ' BLACK MESA ' logo appears, system freezes then multiple freezes occur during the Intro / Credits.
• Gamepad non-functional in parts of Intro-credits then causes 30 second freeze during Gamepad capture.
• • The game tumbles and stumbles along until..
• " Arriving at Sector C Security lab ' Anomolous Materials' after this the Graphics and gameplay are pretty spot on.
• Better than the Linux version.
• Pressing [ Start ] on the Logitech F470 Wireless gamepad releases the default kDE Plasma Mouse pointer that can travel between both monitors.
• Depressing [ Start ] again resumes gameplay.
• I cant put my finger on it but the overall gameplay is more attractive than the Linux version.
• Example: the NPC Character faces look much better. ( I think from memory )
• From what I've played sofar the game is absolutely playable and superior to the native Linux port but its just getting there and the lack menu graphics /functionality.

I can confirm the same issue as OP on Linux Mint 20.2 (Ubuntu 20.04), including on Proton Experimental (tested today) and 7.0-2. However, it's not quite as severe for me.

With regards to no menu appearing (@pcfirebeats issue #5060), launch the game with launch options -oldgameui. The new UI does not work under any Proton version I've tried (and isn't available in the native Linux build at all).

Confirmed: same experience as @lunalucadou and previous posters.

Note that in addition, the game does not work in surround sound. When setting sound to 7.1, only front l/r speakers output sound. If sound pans to any other channel, it simply becomes inaudible. Any workaround or tweak that will get surround sound working? Did anybody have any luck with this?

Tagging @ColdPie1, who was able to solve surround sound issues back in 2020 and mentioned over in the "Surround sound support?" thread he might be able to help. Are you still around?

I tried putting DSOAL (dsoal-aldrv.dll and dsound.dll, both 32-bit and 64-bit variants) in the same folder as bms.exe to no avail. Proton-GE 7.29. Also tried running from Lutris with the "Disable Lutris runtime" and "Prefer system libraries" options.

Log from running Black Mesa with PROTON_LOG=+pulse,+mmdevapi,+dsound,+xaudio2,+winmm in a fresh Proton prefix, using Proton Experimental:
steam-362890.log

I think this is a source problem in general, not just Black Mesa. I have the same problem in a mod Zero Entropy. The text in menus and subtitles is corrupted in the same way

Same thing in Empires Mod
Hoping for a fix

If anyone found some workaround yet, let me know

EDIT: since some time this is no longer an issue in empires mod, I guess the proton replaced the fonts, but they are not the same as in windows (its lacking symbol characters)

Same thing in Empires Mod Hoping for a fix

If anyone found some workaround yet, let me know

If I remember you could work around this by installing the fonts manually into the prefix. This was some years ago I tried it but I think it worked for source based games.

I have the same problem with the source engine games running on Proton, installing the following fonts with protontricks seemed to solve these ugly font issues (at least for me): corefonts (fixes the HUD from using serif), tahoma (fixes captions) and lucida (fixes the console)