T-Mobile celluar update is required yet I have no mobile service

Carrier Update (Required): Released by your Cellular Service provider (Carrier Update), affects your Outgoing / Incoming calls, SMS, Data etc..

How to Update Carrier Settings

You can manually check for and install a carrier settings update with these steps: Make sure your device is connected to a Wi-Fi or cellular network. Tap Settings > General > About. If an update is available, you'll see an option to update your carrier settings.

Update your carrier settings on your iPhone or iPad - Apple Support

Before updating to the latest iOS 13.5.1 as told on your post what was your earlier iOS version. Then you can look into the iOS changes that has happened between the earlier version on your iPhone and this new version that you have updated now. 

This will give you a broader idea of the issue, if it is directly linked to the iOS version or is triggered by something else.

Because iOS 13.5.1 was only for security update, you may probably be carrying a legacy issue from previous iOS versions.