It actually does appear that Mastodon doesn’t know how many replies there are until it loads them for display. Glitch, a Mastodon fork with some UI enhancements has an option to display an estimate of the number of replies. Lemmy obviously displays an exact comment count while using the same protocol. There may be a performance/efficiency motivation for this.
A trending feature should probably have the option to include federated content, as some instances are very small, even single-user.
I find the stance taken by Mastodon’s developer and many users… I’ll be charitable and say unreasonable. It’s about a dozen lines of code to add a proper search and there are two ways to do it (Postgres text search is easy, Elasticsearch may be better for big servers). Some server admins have implemented this.
I’m seeing that for both follows and followers.
There are other ActivityPub Twitter-alikes that may meet your needs better, such as Akkoma. Akkoma has reasonable search, can show remote follows and followers, and seems to keep accurate reply counts. It’s not as polished looking though.