Here's the feedback I got from the Textra support team. I believe my problem was related to "T-Mobile Solution 2", but time (and missed text messages) will tell. Hopefully others will find this useful:
Check in your stock / pre-installed messaging app by long holding on a message bubble (that was missing in Textra) and select Show Details, if it says "Advanced Message" or "Chat" or "File Transfer" then this is what's referred to as an RCS message, it's not an SMS or MMS message.
That's the issue, although really it's a half baked Android implementation if you can receive messages in an inactive app (stock) and not get any notifications, right!? It's also your MOBILE CARRIER trying to lock you in to their messaging app, not good.
AT&T: You can disable RCS messages to you in your stock Messages app under Settings > Advanced Messaging > Use Advanced Messaging = OFF (make the stock app the DEFAULT app first in order to be able to change the setting).
T-Mobile Solution 1: On some phones, you can disable RCS messages to you in your stock Messages app under Settings > Enhanced messaging = OFF (make the stock app the DEFAULT app first in order to be able to change the setting).
If this setting is not appearing, do the following:
From any Home screen, tap Phone.
Tap the MORE icon.
Tap Settings.
Tap Voice over LTE settings.
Select "Do not use VoLTE"
T-Mobile Solution 2: See
https://support.t-mobile.com/docs/DOC-34224#steps2 (set WiFi calling to OFF).
T-Mobile Solution 3: Some users report switching to the pre-installed app, making it the DEFAULT and then switching back to Textra and making it the DEFAULT works.
T-Mobile Solution 4 (digits): Android Settings > Cloud and Accounts > Multi-line settings (tap the 3 dots in the top right corner for more options) and select "log out"
Verizon: Messages+ > Settings > Delete Account (for Integrated Messaging Services)...enter your number and delete. OR Android Settings > Apps > Messages+ > [UNINSTALL UPDATES]