Thank you for reaching out. I can certainly understand your concern with not being able to install stuff from the Google Play Store on your Galaxy watch 4, and I would be happy to look into this further for you. As you are experiencing symptoms with the Google Play Store, I was able to locate a support topic regarding similar symptoms on the Google forum: https://support.google.com/wearos/thread/142526042/google-play-store-not-working-on-galaxy-watch-4?h...
Another reason you could be experiencing these symptoms on your watch is if the storage on your watch is too full. I would recommend checking the storage available on your watch.
If you have tried the troubleshooting provided and are still experiencing, and you have available storage, I would recommend reaching out to Google for further assistance.
If you don't have the proper amount of storage available, I would recommend removing some apps and trying to install the apps again. If you have tried these steps and are still experiencing the next step would be to reach out to Google as well as one of our moderators in a private message with your model number and serial number/IMEI for further troubleshooting assistance: https://bit.ly/3fbRevo
