Like the original poster, I do find that the website search is much better than the app search, and I often go to the web to find things when I cannot find them in the app.
Here is one example of me searching for my own app by name.
On the web it is the first result:
On the app it does not even appear in the first page:
There are a lot of possible discussions about which order apps should be listed when you search for a word, but as a general rule, if I know the exact name of an app I am looking for, and I type it into the F-Droid search, it ought to appear at the top of the list. Sometimes someone tells me of a cool app, and I wonder, “Does it exist on F-Droid?” I search in the app and can’t find it, but then I think, “That app search isn’t very reliable” so I pull up the web page and search there and it is easy to find.