Can domain registrars access your domains emails configured through DNS settings?
Are there any privacy implications to be
mta-sts.tutanota.de. of when configuring a custom domain email with an app like Proton mail?
How do the IP logs work? Would the domain registrar and email service provider both be able to get your IP logs?
No they cannot unless they change the MX records and proxy them (f.x. like Cloudflare Area 1) which would be visible in your DNS settings.
Would recommend familiarizing yourself more with what DNS is and how it works. But essentially it is a system that translates domain names into IP addresses, allowing computers to find websites on the internet. So all it does is telling the sending server to which IP it should connect to.