why you should/could use privacy friendly frontends

mainly because:

• most of them don't have a single ad (except maybe a donation link), e.g. invidious, piped, gnutube, are all YouTube frontends that don't sell your information, don't give you annoying ads you can't block, and:
• most of them are not being run in a huge data center by some sort of comercial company that sells data and I mean if they are, how would it be worse than using the official website?
• a lot of them don't require proprietairy JavaScript (code that runs on the client, your computer.)

how do they work?

i.e. LibreX makes a request to Google with your search term, so your IP doesn't have to. This also makes it harder for Google to track you, or any other user, since you all search for extremely varying terms. for LibreX it would be the following scheme: you > instance > google > instance > you. This means that even if you use Tor or some other non-clearweb IP to connect, Google doesn't notice, since they only see the IP of the instance.

but how do I trust other people over i.e. Google?

You simply can't/don't, so instead: host your own!

short post, but a lot of details :)