there is no way to verify they don't actually log anything

To be 100% sure? Host it yourself. There is always a chance the operator violates your privacy, willing or unwillingly.

I trust my folks at sdf as fellow unix hackers.

self hosting is the only way to guarantee logs arent shared.

however it also means that your server address only pulls requests for things YOU look at, not the whole pool of people using the server. imo this is a bad trade off as it would allow the services to track my browsing easily anyway.

personally I would recommend looking at libredirect with a large # of frontend instances selcted & a vpn/tor. these websites normally work without javascript, so assuming you have a privacy focused browser your IP is the only tracking metric they really have. spreading your requests out over different servers whilst using a proxy would make this really difficult to correlate as it would require that mutliple instance operators were malicious & collaborating.

Trusting is good, but.. don't trusting is better..

https://www.privacyguides.org/en/frontends/

Self-host? Or use VPN to connect.

As another commenter said, it's not possible to verify. You'll just have to take each instance's word for it.

Instance lists for some privacy front-ends will point out additonal info, such as if each instance is using CloudFlare or not (this may or may not be useful depending on if you distrust CloudFlare), some other services (like Rimgo, a private Imgur frontend) lets the instance hoster customize the privacy policy. But once again, this is all relying on the instance host telling the truth.

DIY

Use FreeTube with VPN. But you'll have to find a VPN provider you trust, of course. Should be a bit easier.

Piped is good although it is weakened by the Google attacks. It will be back to normal after a while.