Based on my Windows knowledge:
Series and Season Cover Art for TV Shows are always stored in the location defined in "Options > File Location > Cover Art". Episode Cover Art is always stored next to the video file.
When you do an in-place upgrade from MC24 to MC25 and the installation process finds the previous version, it will copy these files in the MC24 location to the MC25 location. If the installation process doesn't find the previous version of MC, which happens for me most upgrades, these Cover Art files are not copied across. A Library Backup doesn't include these files, so if you have to Restore a Library Backup to get your Library into MC25 after a major upgrade, then the files won't have been copied.
So, what you have to do now is find the location that MC24 used for these files, as per the above setting, and copy them to the correct location for MC25, which will then use them for your Video/Show Views.
For the above reason, I moved the Cover Art location in MC settings to a non-version-specific location a long time ago. All my MC installations, even when I have two versions still installed, use the same Cover Art locations now, and I never have the above issue. Note that the new version of MC still needs to build thumbnails for the Cover Art again, as the thumbnails database isn't migrated from the earlier to the later version.
Note that if you edit the Cover Art location in "Options > File Location > Cover Art", MC will copy (or move, I forget which) the Cover Art to the new location. So you could just edit that setting to point at a non-version-specific location using MC24, and then change it in MC25 to the same location, and MC25 should find all your old Cover Art.
If you need to copy the files over manually, I can't help you with locating or copying Cover Art files under Linux, but I'm sure you will work that bit out.