We have Google one-click signup though. Why is it such a painful process for you (genuinely curious to hear from you)
https://hn.algolia.com/?q=signup+required
In more detail: because life is short, and most of these sites just aren't that great anyway. You may say it's one-click but the fact is users have been gaslit too many times by signups that require multiple interactions to plod through (from surveys to emails to ToS pages that of course no one has time to read). Again, just to find out what the site supposedly does or it's worth their time. After a point it's like, forget it, they're all guilty until proven innocent.
The concern about bots is entirely understandable, and I don't have any immediate answers for you as I have no idea what the current space of countermeasures looks like these days, but it may be worth taking another look at. You might also consider a hybrid approach, that offers say 10 free searches before requiring a signup (so people can get feel for the UX, does it do what it says, is it responsive or is it another piece of React garbage, does it blast them with ads and popups, etc).
And this is the only step, no further questions asked! For the 10 free searches that's a clever thought. But it still can be botted by using different browser sessions, vpns, proxies etc... Perhaps I'm being extra careful as well, but I heard some bad stories of bot attacks around me.
Anyway I appreciate you taking the time to explain your thoughts!