I assume that your watch face is a standalone app, i.e. it doesn't require an app to also be installed on the phone. If you're not sure take a look at the "Specify an app as standalone" section in the documentation.
Standalone apps for Android Wear 2.x and above (this includes Wear OS) can't be installed via the phone. You have two options:
- Use the Play Store app on the wearable device
- Go to the Play Store desktop website and select your wearable device as the install target
In other words, what you're experiencing is the expected behavior.
If you really want your app to be installed from a phone (or if you're targeting Android Wear 1.x) it has to have a phone app. From the documentation:
For Wear 2.0
On devices running Wear 2.0, when a user installs a phone app that has an associated watch app (either an embedded APK or an APK uploaded via the Play Console), the user gets a watch notification about the available watch app. Tapping the notification opens the watch Play Store, giving the user the option to install the watch app.
For Wear 1.0
Wear OS now allows you to distribute your Wear app the same way for both Wear 1.0 and 2.0. When a user installs your phone app, if you have a compatible Wear app in the Play Store, it will automatically be installed on Wear 1.0 watches.
However, I strongly advice against doing this for the sole purpose of discoverability on the phone.