I may be confused.

Is the following correct?

You have a new (12) phone with Textra as the default texting app.

You have apps from your old device that are also receiving the same texts, although the apps are not set up yet.

Yes?
I have understood?

If so, I assume that you used some backup method to transfer apps and data to the new device?

That alone may have set up the other texting apps enough for them to pick up the texts.

And yes, when more than one texting app exists, they can all get the same texts, even if they are not the default app.

That way, if you decide to change defaults, your messages are not lost and there is no need to transfer anything.

I discovered this when bouncing back and forth between two third party and the stock messaging apps.
I too thought that it was odd, but it worked, so I let it be.

What is your issue with this, are there notifications or something else from the apps that are not default?

 

This may not be relevant, but there's a default setting that allows a link (I know, not a message) to open a default app that's not actually installed. Perhaps your account is opening what you have used previously.

Google Play Instant

https://support.google.com/googleplay/answer/7240211?hl=en-GB

Play Store app - Settings - General - Google Play Instants

 

Yeah, that Google Play Instant is some sneaky crap.

I trust NOTHING Google and this is definitely one that I rid any device of immediately.

Not only is there the setting that @Madd61 mentioned, there is an app as well- one that Google PlayStore will download automatically if PlayStore is not disabled entirely- each time the device gets a 'security update' (code for "Google wants to mess with your device").
It is called Google Instant Apps.

I am not sure if it is prevented from downloading if you have autoupdate turned off, but it seems that even with this setting off the stupid thing would reappear at random (whenever Google messed with my device at 2AM) and disabling the PlayStore altogether was the bullet proof solution.