I still have no idea what the root cause is, but it's probably related to this at line 4431 of the Proton log:
41405.645:0140:0198:err:virtual:try_map_free_area mmap() error メモリを確保できません, range 0xf7fe0000-0xb60000, unix_prot 0x3.
41405.645:0140:0198:err:virtual:try_map_free_area mmap() error メモリを確保できません, range 0xf7fe0000-0xb60000, unix_prot 0x3.
41405.645:0140:0198:err:virtual:try_map_free_area mmap() error メモリを確保できません, range 0xf7fe0000-0xb5e000, unix_prot 0x3.
41405.645:0140:0198:err:virtual:try_map_free_area mmap() error メモリを確保できません, range 0xf7fe0000-0xb5e000, unix_prot 0x3.
41405.645:0140:0198:trace:seh:dispatch_exception code=e06d7363 flags=1 addr=7B011197 ip=7b011197 tid=0198
41405.645:0140:0198:trace:seh:dispatch_exception info[0]=19930520
41405.645:0140:0198:trace:seh:dispatch_exception info[1]=5787ee90
41405.645:0140:0198:trace:seh:dispatch_exception info[2]=001733c4
41405.645:0140:0198:warn:seh:dispatch_exception EXCEPTION_WINE_CXX_EXCEPTION exception (code=e06d7363) raised
41405.645:0140:0198:trace:seh:dispatch_exception eax=5787edd0 ebx=e06d7363 ecx=00000000 edx=5787ede4 esi=5787ee6c edi=5787edec
41405.645:0140:0198:trace:seh:dispatch_exception ebp=5787ee38 esp=5787edc4 cs=57870023 ss=002b ds=002b es=002b fs=0063 gs=006b flags=00000203
"メモリを確保できません" means "Cannot allocate memory" in Japanese. (the system language/locale is set to Japanese)
If the game's memory allocation code is problematic in the first place, but only results in an error on Linux, I might be able to get in contact with the developer to figure things out. Do we even have any information here that might be useful to them, though?
Apparently the game works fine on Steam Deck, so uh... what? Is something wrong with my system? https://twitter.com/bibresin/status/1595963299191222273
Okay, I figured it out, it's the screen resolution. I tried 1280x720 (close to that of the Steam Deck) and 1600x900, and in either case the error does not occur. It does occur at 1920x1080 and above though. That explains why it works fine on the Steam Deck.
I already let the developer know of this, but I still don't know whether it's the game or Proton being weird here.
Also, just to be sure, I also ran the game on Windows natively on my laptop (2560x1440 display), and there it works just fine at native resolution.
Nothing extracted yet.
Compatibility Report
System Information
I confirm:
Proton log: steam-1736300.log
Symptoms
Game crashes at the loading screen after starting a new game. This dialog appears when it crashes:

Reproduction
Run the game through Proton and do "New Game" at the title screen.