After following the instructions in https://steamcommunity.com/app/366250/discussions/0/3368153731094314666/?ctp=2#c3758850762507155525 I can successfully launch and complete the main missions without issue.

Looks like the d3dcompiler_46.dll file is missing from Metal Slug - I did the same as the OP that I copied the file from my Metal Slug 3 into Metal Slug folder then everything just works. Did not change any of the resolution and compatability settings.

The game file location: /home/deck/.local/share/Steam/steamapps/common/Metal Slug 3/d3dcompiler_46.dll → copy to /home/deck/.local/share/Steam/steamapps/common/METAL SLUG/