How do I keep Safari from auto-launching an app?

Short version: you don't.

Apple provides a mechanism for app developers that let them associate specific domains/URLs to the app. If you subsequently visit a site/URL on that list, Safari will (optional, depending on how it's setup) switch to the app, or ask you if you want to use the app instead.

The fact you have their app installed, combined with the fact the developer has configured their app to intercept/handle requests for their domain(s) is what's triggering this. Short of removing the app, there isn't much you can do.

It's covered under the Developer Documentation at: Allowing apps and websites to link to your content | Apple Developer Documentation

I suggest that you contact those apps developer/support teams, explain your problem, check those apps configuration, and ask them for a possible solution.

Regards

Giulio

If you want to force a link to open in Safari and not open the app associated with that link, you can "long press" the link and choose Open from the contextual menu that appears.