You can simply download your emails from Tutanota, make a proton account, pay for their plus plan, switch the NameCheap registrar account email to the proton one you made, and connect the domain. The only account tied with that company will be the account you own the domain with.
It is usually recommended that you use the email they give you because in some cases people have been screwed over because their domain expiry emails were sent to their custom domain, but they didn’t renew mail hosting so they never received the email and don’t realize until it is auctioned off.
The only accounts I don’t use with my own domains are the domain ones (NameCheap, Netim) and my password manager (Bitwarden) in case I have configuration errors and can’t send/receive emails like login alerts or attempts.
If you do decide to use Tutanota email address for your NameCheap account and have your emails hosted by Tutanota then later switch to Proton, you will need to change DNS settings to Proton’s anyway. These services also give you a default account you can not remove because they don’t want to lose you as a customer when your domain expires, they still want your business.
In this video the email address is created as an alias. I’m scared that if I do that, when I will switch, I’ll no longer be able to use the username I took in the new service.
I buy example.com at porkbun (I will use porkbun or cloudflare)
Link it to tutanota
Use “hi” as my username for the alias (firstname.lastname@example.org)
After two years I switch to protonmail and delete my tutanota account
I link my domain name to protonmail but I’m not able to use “hi” as my username because it’s already taken
That is not how it works. As you are the owner of the domain you control all of it. If you use email@example.com in Tutanota and then switch to Proton Mail you just create firstname.lastname@example.org again.
The service can’t prevent you from re-creating an email address with your own domain, the only time they can do this is if it is their own domain.
Don’t worry about not being able to re-create an email address with a different service, I have done it before and there was no issues because, as I have said, the service can’t control you use of your domain at another service.
Hope this helps!
Edit: The joy of having a custom email domain is if the service you are using shuts down, all you do is edit the DNS records for your domain, point them to a new service, and then re-create all your email addresses and you are back up and running again.