Why does Safari frequently log me out of websites?
This seems to be a common issue (which I also experience). I know that Safari is particular with how it handles cookies, which is a likely cause. I'm assuming this is on Apple's radar.

I have some suspicion that it's because I have website tracking completely off, but never tested it fully as I prefer to have it off.

As a temporary fix, the use of a password manager (iCloud Keychain is built into Apple devices) makes the login process faster.