The problem is the same for both of those errors: you don’t actually have the mode you’re trying to play installed, even if Steam is telling you it’s installed. You can verify this for yourself by right-clicking the app of the mode on Steam, selecting Properties… > Installed Files, and checking if the size of installation is "0 B", as that would indicate the mode isn’t actually installed and that Steam has bugged for that app. If Steam got bugged for the app, then attempting to verify integrity of game files for the bugged app would result in nothing getting fixed. My guess for it getting bugged on Steam is: attempting to start a mode that isn’t installed while having a different mode of the game installed, thus preventing a different error, which then makes the Plutonium program attempt to start the mode that isn’t actually installed, finally somehow resulting in Steam counting the game as installed even though it’s not.
The mentioned files in those errors are part of code_pre_gfx_mp.ff and code_pre_gfx_zm.ff according to their zone source files. Missing the mentioned file corresponding to a mode usually indicates the mode isn’t actually installed at all. Starting a mode makes the Plutonium program attempt to load the respective mode’s files, thus, for example, if you don’t actually have Multiplayer installed, the error would generate due to missing the code_pre_gfx_mp.ff file. Just a note, the error wouldn’t get generated for missing the opposite mode’s file from the one you’re trying to start.
When this happens to other people, I usually suggest—from my comment in the following post—the instructions under “If none of the previous suggestions have worked”, as following those instructions makes Steam think the game isn’t installed, thus allowing you to install the mode without uninstalling any of the files. Here’s the post: https://forum.plutonium.pw/topic/34150/cant-play-plutonium-error-during-initialization-missing-config-file-default_mp_controls-cfg-during-initiliazation-may-need-to-add-to-code_pre_gfx/2