I want to use the most basic Bulk Redirect to redirect all URLS from one domain to another. Specifically, www.fffilm.cz/any/path.html should redirect to www.fffilm.name/any/path.html.
You need Preserve path suffix checked as well. Perhaps the wording is a bit confusing there, but it basically takes any of the path that isn’t matched (in your case, the entire path) and copies it over: How Bulk Redirects work · Cloudflare Rules docs
As cbrant said, you also do have another rule redirecting from https://fffilm.name/ to https://www.fffilm.name/, but that one seems to respect/copy paths. It would still be more efficient to directly redirect to www though.