Any WP Search “?s=xxxx” starts processing JS/CS

Assets will be generated whenever a page has different css or js file names, it doesn’t care if it’s search or some other page.

If you have a lot of files being created on search pages, check what is on the list.
Likely, one or more files is different on every search you are doing.

You should exclude the dynamic file from minification, or ideally, fix your code so that the enqueued file url never changes, or only changes when needed. If a file name changes every time, FVM sees a new file every time.

You can minimize the cache directory by disabling merging, which will then minify each file individually. But then, if 1 file is changing, that file is always still going to be regenerated unless you either fix the url, or exclude it.