There's a confusion going on when managing client apps, that you should have a developer account. You don't need one. When managing clients app store apps, client should own a developer account, and they should invite you to the team.
To see the best role possible for your position, here's a good table overview.
For example, if you manage app release process to the TestFlight, client will add you to the team with App Manager role. Process is to login to App Store Connect, go to Users and Access, add a new users. Select app manager role, check Access to Certificates and also generate individual keys for access to the App Store Connect API. That's it. No need for your own developer account, just your email address.
