Wow, you write longer posts than I usually do, and that is saying something! I accept the challenge!
So I won't quote you but will try to address some of the issues.
First, the only time I know of that a movie Cover Art image is placed into the "Videos" directory is when the disc has been inserted and the Cover Art has been collected via the "Get Movie & TV Info" function or "Get from Internet", or other Cover Art function, and as the art can't be saved next to the movie file, because the movie file is anand optical disc, it is saved into the "Videos" directory.
So if you rip a Blu-ray or DVD before collecting Cover Art, then the images should be saved next to the movie file. If the Cover Art has been stored in the "Videos" directory for the above reason, and then you run the "Get Movie & TV Info" function, I think MC will get another copy of the image and save it next to the movie file.
Note that I rip using DVDfab directly, and don't rip from within MC. If you do rip from within MC, and have the setting "Get cover art from internet after ripping" ticked, maybe MC does put the image into the "videos" directory. I haven't tested that, but it shouldn't, because it should already have created the movie directory, and should put it in there. I guess what actually happens depends on the workflow you use.
You can check where the Cover Art is stored for a movie by looking at the [Image] tag, or more correctly the [Image File] tag, for the movie. That isn't an editable field. As you say, MC chooses where to store Movie Cover Art. You can't change it. I believe the functionality has been the same since I started using MC back on MC18. The "TV Logos" Cover Art directory is a reasonably recent addition, and whether the "Albums" and "Artists" Cover Art directories exist or are used depends on your Cover Art settings for audio.
BTW, I wasn't suggesting creating a "Movies" directory under the Cover Art directory and storing movie images in there. All Cover Art for video files should sit next to the video file itself, in the same directory. The only exceptions are when the video file is on an optical disc, and with TV Series and Season Cover Art. Cover Art for TV Episodes, which are the actual video file, are also stored next to the video file in the same directory.
If you are ripping Blu-rays from within MC, then the rules for which directory the movies are placed in are defined in the "Options > File Locations > Ripped BD Video > Folder Rule" setting. The default may have changed between MC21 & MC22. Or you may have changed the rule. The default rule in MC24 is "BD Movies\[Name]\".
The files and folders under the movie's directory don't really matter too much, as long as the movie plays, leave them alone. There may be just a BDMV directory with several sub-directories, or there may be another directory next to the BDMV directory. Includsion of the CERTIFICATE is a reasonably recent change with MC I believe, and ensure Blu-rays work properly with more recent movies and Windows updates, from memory. The "index.bdmv" file is what MC points to and "plays", and so the Cover Art image file should be called "index.jpg" for all Blu-rays that have been ripped to a folder structure. That is why all folder structure Blu-ray rips must be in their own directory. That is why the name of the directory that a Blu-ray rip resides in must be unique, and how rips and Cover Art can get messed up if two movies with the same name are ripped using the default folder naming rule as above, "BD Movies\[Name]\". I always add the year to the end of the movie name, to make the folder name unique. i.e. I rip to (or move a rip to) the structure "\Movies\[Name] ([Year])", as per the Cape Fear example I used above, "\Cape Fear (1962)\".
Note that the actual Cover Art file of a folder structure Blu-ray rip for the 1962 version of Cape Fear should be, using my structure; "\Movies\Cape Fear (1962)\BDMV\index.jpg", sitting right next to the "index.bdmv" file.
If you ripped Blu-rays of both Cape Fear versions to the same folder, "\Movies\Cape Fear\" or similar, and ripped the 1962 version second, then the "index.jpg" Cover Art file will be for the 1962 version, and unless MC did some magic in the naming of the \BDMV\ folder, the 1991 version of the movie could be broken. Does it still play?
As you have uninstalled all versions of MC prior to MC24, clean up those old MC directories. You don't need them.
Cover Art is linked to a movie via the [Image File] tag, shown in the MC Tagging Window as just "Image". Most of the time when you are looking at an image related to a movie, you are actually looking at a Thumbnail of the image. Thumbnails all reside in one indexed file so that is very fast to read. So when you load a View of movies, MC looks up the [Image File] tag for each movie, which includes the full path, and then it retrieves the Thumbnail using that tag information as the index to the thumbnail. So it is fast. (Actually, I think MC uses an internal file index number rather than the fule [Image File] tag information. But same sort of process, only even faster.)
The "Options > File Location > Cover Art > Folder" setting doesn't apply to Video files. It applies to audio files (Album, Artist folders), TV Logos, Genres, TV Series and Seasons, Videos where the normal rule can't be applied (i.e.Optical discs not ripped, but imported into MC) and other File types.
No, you can't move Movie Cover Art files to wherever you want to, as mentioned above, the [Image File] tag stores where the Cover Art is, and it can't be edited. The only exception I know to this is if you use the Cover Art "Add from file..." function to add Cover Art to a movie, and then answer "No" to the question about copying the image to the specified location, as per the dialogue shown in the attached image. If you answer "Yes" for a movie, MC will copy the selected file into the directory next to the movie file, and not into the directory specified in "Options > File Location > Cover Art > Folder". In other words, MC follows its own internal rules if you let it copy the file.
Read the Wiki article on the
Rename, Move, and Copy Files function. Read it
very carefully. Test it with small numbers of files, or in a test database. It is a very powerful tool.
The RM&CF function, as it is known, is used to move any media file MC knows about in its library, and can rename file and/or folders using naming rules. It also renames and moves associated file, such as Cover Art and Sidecar files. So, for example, I have rules for movies where;
The Base directory is set as "F:\Movies\"
The Directory rule is set as "[Name] ([Year])\"
The file name (for file-based movies - MKVs, AVIs, etc., not optical disc rips) is also set as "[Name] ([Year])"
Which makes my movie directory and filenames unique, which is good. Actually, there are a few instances where movies of the same name came out in the same year, which would cause an issue, but I haven't hit any of those yet.
You would have to share the full path and file name of the "Get Carter" and "Cape Fear" movies for me to comment on why one worked and the other didn't. But I suspect it is something to do with a folder naming difference.
I think that about covers everything you mentioned.
PS: I didn't properly proofread everything above. Hopefully, there aren't any significant blunders!