How to install app from beta track on Wear OS smartwatch?

I created a standalone smartwatch app for Wear OS. I use a Huawei Watch 2 4G for testing. I now want to have it in the beta track on Google Play Store so that users can test it. I've created some smartphone apps already and put them in the Play Store, so I'm used to the process. What I did so far:

Created entry on Google Play Console
Added a release to the open beta track
Filled all necessary stuff
Published the app and got the URL to participate in the beta test
Opened the URL while logged in with my test account and agreed to become a tester
Wiped the smartwatch and copied the same account to the watch during setup

Now I don't know how to install the app from the Play Store. On a smartphone I would simply open the URL in a browser and would be able to install it from there. What I tried so far:

Searching for the app name and for the package name on the Play Store on the smartwatch, but it can't find it.
Opening the Play Store entry in a browser and click the install button, but it says that I have no devices.
Opening the URL on the paired smartphone, but it only says that the device is not compatible.

How can I install a standalone Wear OS app that is in the open beta track on Google Play Store?

Solution

As suggest in @tofferj 's comment I simply had to wait a few more hours. I'm now able to find it by simply searching for the app name in the Play Store on the smartwatch.

Seems like the status "published" on the Google Play Console doesn't mean that it's already in the search index.