When opening some code files (ie. PHP, HTML, Twig, etc.) Kate sets the tab width and indentation width to 2, even though in the Kate configuration, I've set it to 4. It doesn't happen with all PHP files, only some, however, a given file will always open with the same (incorrect or correct) indentation every time. I can provide sample files that open one way or the other, although, I cannot figure out how Kate is determining what tab settings to use. I've renamed the files to no effect. I've also edited the files so that they have the same content, and Kate still opens with the (incorrect or correct) tab settings per file.
The default tab setting in kate is over ridden by special comments in the file, .kateconfig and .editorconfig files. These comments and config-files specify these settings. Could it be that you have some of these comments or config files?
Ugh, yes it turns out to be a stray .editorconfig way up the directory tree. It looks like this is desired behavior, and I apologize for not knowing of this possibility. I can set this as resolved:invalid or whatever status makes sense for my bogus non-bug.