• Signed up for D&D Beyond
• Downloaded DnDLauncher.exe
• Added DnDLauncher.exe to Steam library as a non-steam game.
• Changed settings to use Steam Proton for compatibility with Windows (which works for BG3).
• "Play"
• Black window with activity indicated.
• Second window labeled "Dungeons and Dragons Launcher" displays error message: "Dependency Installation Failed."
• Close either window, nothing follows.
• Try running separately from Wine and get crashdump:

Unhandled exception: page fault on read access to 0x0000000c in 64-bit code (0x00000001400fcb7c).
Register dump:
 rip:00000001400fcb7c rsp:000000000029d490 rbp:000000000029f220 eflags:00010206 (  R- --  I   - -P- )
 rax:0000000000017ef0 rbx:000000000029f268 rcx:000000000029f268 rdx:0000000000018000
 rsi:000000000029f120 rdi:0000000000000000  r8:0000000000000100  r9:0000000019930520 r10:0000000000016d90
 r11:000000000029d7c0 r12:0000000000000000 r13:000000000029d5a0 r14:000000000029fea0 r15:000000000029e008
Stack dump:
0x000000000029d490:  0000000000000001 000000000029d750
0x000000000029d4a0:  000000000029f120 000000014079ce50
0x000000000029d4b0:  0000000000000000 00000001405cae08
0x000000000029d4c0:  0000000000000000 000000014060fee1
0x000000000029d4d0:  0000000000000000 000000000029f120
0x000000000029d4e0:  000000000029dea0 00000001405cad49
0x000000000029d4f0:  000000000029d5a0 000000000029f120
0x000000000029d500:  000000000029dea0 000000000029d750
0x000000000029d510:  000000000029ec20 00000001405cd290
0x000000000029d520:  000000014060fe60 000000000029f220
0x000000000029d530:  000000000029f220 000000000029d868
0x000000000029d540:  000000000029ec20 00000001405cc3b2
Backtrace:
=>0 0x00000001400fcb7c EntryPoint+0xffb338bc() in dndlauncher (0x000000000029f220)
  1 0x000000014060fee1 EntryPoint+0x100046c20() in dndlauncher (0x000000000029f220)
  2 0x00000001405cd290 EntryPoint+0x100003fcf() in dndlauncher (0x000000000029d750)
  3 0x00000001405cc3b2 EntryPoint+0x1000030f1() in dndlauncher (0x000000000029d750)
  4 0x000000007bc525a5 EntryPoint+0xffffffffffffffff() in ntdll (0x000000000029d750)
  5 0x0000000140516dcb EntryPoint+0xfff4db0a() in dndlauncher (0x000000000029f4a1)
  6 0x000000007bc52780 EntryPoint+0xffffffffffffffff() in ntdll (0x000000000029f4a1)
0x00000001400fcb7c EntryPoint+0xffb338bc in dndlauncher: movl    0x000000000000000c(%rdi),%esi
Modules:
Module    Address                    Debug info    Name (33 modules)
PE            7b000000-        7b3fd000    Deferred        kernelbase
PE            7b600000-        7b969000    Deferred        kernel32
PE            7bc00000-        7bf3c000    Dwarf           ntdll
PE           140000000-       140961000    Export          dndlauncher
PE           1c8db0000-       1c9097000    Deferred        msvcrt
PE           1cd860000-       1cd86f000    Deferred        api-ms-win-crt-utility-l1-1-0
PE           1d97a0000-       1d97ae000    Deferred        api-ms-win-core-fibers-l1-1-1
PE           21a7e0000-       21a9ce000    Deferred        setupapi
PE           231ae0000-       231d60000    Deferred        rpcrt4
PE           23d820000-       23dfc2000    Deferred        user32
PE           241850000-       24185e000    Deferred        api-ms-win-crt-environment-l1-1-0
PE           262250000-       262260000    Deferred        api-ms-win-crt-runtime-l1-1-0
PE           26b4c0000-       26bbb9000    Deferred        gdi32
PE           2739c0000-       273ec9000    Deferred        oleaut32
PE           28ba60000-       28ba6e000    Deferred        api-ms-win-crt-time-l1-1-0
PE           2e3540000-       2e364f000    Deferred        shlwapi
PE           2e8f10000-       2e948f000    Deferred        ole32
PE           2f1fa0000-       2f1fbe000    Deferred        version
PE           30a2c0000-       30a2d0000    Deferred        api-ms-win-crt-stdio-l1-1-0
PE           30c980000-       30c98f000    Deferred        api-ms-win-core-synch-l1-2-0
PE           3126f0000-       312744000    Deferred        shcore
PE           327020000-       3271a4000    Deferred        combase
PE           32a700000-       32a7bc000    Deferred        sechost
PE           330260000-       330387000    Deferred        advapi32
PE           33ea00000-       33ea10000    Deferred        api-ms-win-crt-string-l1-1-0
PE           344840000-       34484f000    Deferred        api-ms-win-crt-filesystem-l1-1-0
PE           350a30000-       350a40000    Deferred        api-ms-win-crt-convert-l1-1-0
PE           355100000-       35510f000    Deferred        api-ms-win-crt-locale-l1-1-0
PE           360a80000-       360a91000    Deferred        api-ms-win-crt-math-l1-1-0
PE           39b510000-       39b51f000    Deferred        api-ms-win-crt-heap-l1-1-0
PE           3af670000-       3af9dd000    Deferred        ucrtbase
PE           3afd00000-       3afd62000    Deferred        imm32
PE        74e704820000-    74e7050f2000    Deferred        shell32
Threads:
process  tid      prio (all id:s are in hex)
00000038 services.exe
    0000003c    0
    00000040    0
    0000004c    0
    0000006c    0
    00000084    0
    000000a0    0
    000000c4    0
    000000c8    0
    000000d4    0
00000044 svchost.exe
    00000048    0
    00000054    0
    00000058    0
0000005c winedevice.exe
    00000060    0
    00000070    0
    00000074    0
    00000078    0
00000064 explorer.exe
    00000068    0
    0000009c    0
    000000ac    0
0000007c plugplay.exe
    00000080    0
    00000088    0
    0000008c    0
    00000090    0
    000000b4    0
00000094 winedevice.exe
    00000098    0
    000000a4    0
    000000a8    0
    000000b0    0
    000000c0    0
000000cc rpcss.exe
    000000d0    0
    000000d8    0
    000000dc    0
    000000e0    0
    000000e4    0
    000000e8    0
000000f0 (D) Z:\home\user\Documents\My Games\SIGIL\DnDLauncher.exe
    000000f4    0 <==
    00000100    0
System information:
    Wine build: wine-6.0.3 (Ubuntu 6.0.3~repack-1)
    Platform: x86_64
    Version: Windows 10
    Host system: Linux
    Host version: 6.8.0-52-generic

You're using Ubuntu's pre-packaged WIne which is ancient.  Try installing Wine from directly from WineHQ:  https://gitlab.winehq.org/wine/wine/-/wikis/Debian-Ubuntu

I purged the older pre-packaged wine and then manually installed Wine 10 from the winehq.org repository.

It got slightly further... Instead of a crash dump, after the initializing screen it creates a solid black rectangular window with no buttons or text.

edit: messing around with wine manually is kind of a pain, which is why I was hoping it would run through Steam Proton...

I have been looking it as well.  It seems that Sigil needs WebView2 which is still kind of not supported by Wine.  I have read that if you install the mono-complete package should help with that.