I use Fastmail with a specific domain and/or aliases to separate it easily by rules as needed. But I do pay for Fastmail and only send emails to myself so may or may not be applicable to you.
Yes, you can configure a DNS server (or better - two) that serves as an authoritative server for local.mydomain.com and forwards everything to the global DNS servers (eg 8.8.8.8, 8.8.4.4 and 1.1.1.1). You have to use these DNS servers on your devices on a local network (manually or to configure DHCP server to advertise them). I did with BIND because this is what I know but other DNS servers will probably work too.
Quite a bit of stuff: Fastmail, domain registrar, Spotify, Netflix, Prime Video, Apple TV+, Microsoft Office 365 Family subscription (includes 1 Tb storage for 6 family members), GitHub copilot.