Excessive file creation different issue?

One of my WP installations has a few million (!) files in the W3TC cache directory here:

wp-content/cache/page_enhanced/www.rustelozebenen.org/search/{search_term_string}

There is a directory there named {search_term_string}, curly brackets included. In it there seems to be a recursive process going on. There’s directories nested dozens of levels, seemingly centering around four pages: contact, algemene-voorwaarden, privacy-verklaring and nieuwsbrief. Like this:

{search_term_string}/contact/algemene-voorwaarden/privacy-verklaring/nieuwsbrief/contact/algemene-voorwaarden/privacy-verklaring/algemene-voorwaarden/algemene-voorwaarden/privacy-verklaring/algemene-voorwaarden/nieuwsbrief/privacy-verklaring/algemene-voorwaarden/contact/nieuwsbrief/privacy-verklaring/contact/algemene-voorwaarden/contact/algemene-voorwaarden/contact/nieuwsbrief/nieuwsbrief/privacy-verklaring/contact/contact/_index_ssl.html

It goes on to much deeper levels than this. All the cached pages seem to be empty search results:

https://www.rustelozebenen.org/wp-content/cache/page_enhanced/www.rustelozebenen.org/search/%7Bsearch_term_string%7D/_index_slash_ssl.html

I don’t use object caching so it doesn’t seem to be related to this topic:

https://wordpress.org/support/topic/excessive-files-creation-issue/

I use WP 6.5.5, W3TC 2.7.3 and theme GeneratePress. I will upgrade to latest versions, remove excessive files though SSH, and try setting an exception for page caching for URI’s containing /search/ or search_term_string. Hopefully that will help, but I wanted to report this anyway.