I'm not familiar enough with this software, but it seems that it's essentially designed for very very very large amounts of data and fast/instant real-time search. Small instances running on modest servers do not fit in this picture sadly, feels like it's a rather painful blind spot of the project.
At a quick glance, the only relevant issue I found was this
Even on instances where it works I find it not very usable. I'd like to be able to search in certain contexts like my own posts or by a certain user or posts I have seen or faved but these constraints do not seem to exist.
On the instances where search is active, the constraints are that one can only search there own posts (to prevent abuse).
From the documentation: "Mastodon’s full-text search allows logged in users to find results from their own toots, their favourites, and their mentions."
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