Available apps will not install on watch

I'd try a couple of things next:

1. Restart your Apple Watch (assuming it's all set up). This takes a couple of minutes, so be patient.
2. Make sure you have your watch very close to your iPhone when you're trying to install available watch apps.

Also...can you double check to make sure you're signed into the same Apple ID on both your new iPhone and watch? I've seen this happen when there's a mismatch. (For example, I have two Apple IDs, and always have to make sure I'm using the proper one at the proper time.)

And one last thought, since you said this is a new iPhone. Did you Unpair your watch from your old iPhone before pairing it to your new iPhone?

How have you been trying to install apps on your watch?

Make certain you're signed into the same Apple ID on both your watch and iPhone.

Then take a look at this to see how to install apps on your watch:

Get more apps on Apple Watch - Apple Support

If you already have Apple Watch "enabled" apps on your phone, you'll see them in the iPhone's Watch app...scroll down and you'll see Installed Apps, for any you've already got on your phone, and Available Apps, for iPhone apps that have an available Apple Watch app.

Hope this helps.