If I understand it correctly it never let's the "enduser" connect directly to the email accounts. It always has a service in between. That way as far as Gmail or Outlook knows it only gets requests from one or a handful of IP addresses.

That’s the point: a small number of IPs accessing many accounts could become suspicious. (But may not be trivial to distinguish from legitimate usage due to NAT.)

I would assume they probably use tor or residential proxies in order to get around any ip related rate limiting

This is a fair assumption, although to be fair a botnet is essentially a collection of residential proxies.

And yes, Kopeechka controls the inbox, and only lets you see stuff going forward that matches the regex you specify.

Does Tor help here? I thought it’s blocked for clearnet sites

Tor probably doesn't help, but it's not blocked by design.

Tor traffic meets the rest of the internet via exit nodes. There are a finite number of exit nodes and some sites seem to know what they are at a given time and may block the traffic or present a bunch of extra captchas.

Nope, Tor usually makes things worse.

Ask anyone who uses Tor for their day-to-day web browsing. They're often given additional CAPTCHAs and the like. Some sites block them entirely.

Tor might hide where you're coming from, but to any website, it's obvious you're connecting from Tor.