I typically like to keep the registration of the domain itself in the customer's own registrar account (even if I have to set it up for them). I provide them with that information (or they provide it to me, if they have already registered it).

Then depending on the registrar, there may be features that help to facilitate this type of management. Porkbun, for example, has "subaccounts" and also "authorized users" where you can then set yourself up to be able to admin those domains on behalf of your client. Godaddy, as another example, has a feature called "Delegate Access", where you can set yourself up under your client's account to be able to make changes, perform renewals, etc. on their behalf.

I would imagine that other registrars might have similar features.

Thats a good idea. The current domain name registrar I currently use for my customers is iwantmyname (Recommended by fastmail). I asked them about this a few years back but they said they didn't have any kind of delegation system, but maybe I should check with them again.

Did you every have a problem where a customer got confused about the billing for the domain name? I'm pretty good a documenting the things I do regarding email and what needs to happen to keep there email system going, but I often get customers that have no idea about the billing when the domain name bill comes though to their email. They don't seem to remember that it has to do with there email account. Then they ignore the bill, their email goes down, they call me, I remind them that there email depends on a working domain name, they get there bill sorted out and the email gets restored. Some times this process gets repeated with customers that keep forgetting.

You should have another IT professional you can partner with, who you trust, who can facilitate transitioning everyone. Business continuity and all that jazz.