A checkbox in the filter sidebar is a requested feature that, unfortunately, due to how Ao3 is coded, is significantly more difficult than doing it through the search page. I've looked at it, it may happen at some point, but it's a very non-trivial amount of work.

As for the bug you're reporting on mobile, I'm not experiencing that when I test the extension on my Android tablet. If you could check to see if it's still happening, and if it is, send me the search you were performing as well as the information of the android device and version of Firefox, I could investigate it.

One possibility is that for the search you performed, there were no results on that page with your desired ship as the first-tagged ship. As noted in the description, The extension works by getting search results from Ao3, and then going down the results page and deleting all results that don't have the right first ship. This results in fewer results per page. In my testing, I never encountered a case where the number of results on a page was actually zero, but there's no reason why it couldn't happen.

Unfortunately, this is the only practical way to implement this extension, barring a change to how Ao3 is built. I can't control what search results Ao3 returns, just what gets displayed to you.

This is no longer the case!