you need an SMTP server from anywhere. So either get a VPS and use it as smtp server or use cloud (aws, azure, google, ..) and then send it via them. Both work in a good way. I like to use aws SES

And is it cheap? And can i also migrate it so i can use gmail for recieving and sending mails?

yes. For aws SES you get 1000 for free and iirc for each 100 or each 1000 after that 1 cent.

Migrating is also easy, as you can just switch the credentials to a different provider and you are good to go

SMTP server from gmail also works

Have you tried Zoho mail?

Please, please try out migadu mail

im not sponsored but i have 50000k emails it feels like and its just brilliant. its simple and does exactly what it needs to do and the support is very nice in my experience

you can integrate it with thunderbird or gmail, i personally use gmail. i enabled forwarding for all my addresses and i set up the send-as things for all of my mail domains as well and it works flawlessly.