I agree, the search is quite bad.

The UI is bad and the results seem to be poor. I don't necessarily have the issue that emails are not in the results, but more that results are too numerous and the only way I can narrow down results is putting more constrains in the UI. What often happens for me is that I search using a several terms or some specific phrases and the search returns tons of results (does it just do an OR between words in the search) and I then end up clicking (why can't the time constraint be a slider?!) through different months (based on what I recall about the timeframe of the email) until I find the email.

When I was using notmuch I recall results being much better.

Another annoyance is that Thunderbird only seems to search locally, i.e. if I don't have some folders downloaded it will not do a server search as well as a local search (maybe there's a setting for it?)

I submitted a Thunderbird bug 13 years ago now, that Thunderbird doesn't let you just search for a word, and find all copies of that word: https://bugzilla.mozilla.org/show_bug.cgi?id=752844 . Their search instead tries to be clever, but it then finds stupid stuff like (in my case) "The base of Wedding is wed. The plural of wed is weds. Lets return every email ever from a Wednesday"

Still not fixed.

I've been pretty happy with its search and have never had issues finding emails. The UI isn't great and theres a lot of cruft to filter through but it does work...

I have found that "Quick Filter Bar" is often much better at searching if you know which folder the email is in.

It helps to sort the results by date rather than relevance. Relevance is the default and the results are all over the place and it does indeed feel utterly broken :)

I run grep on Thunderbird's storage directory and it's significantly faster than anything Thunderbird itself attempts. (It also allows finding exact matches, fuzzy search without language "awareness" is disgusting to use.)

Sounds like Apple Mail so maybe no one gets it right.