Installing the youtube app on your gos will not compromise your gos system, but you will be strongly tracked through the app's tracking and will be forced to see ads( unless if you have a systemwide adblocker). It will report your ip and associate your activity with other devices in your home (though ip) unless if you always use a vpn with the yt app.
If you are logging into a google account with the yt app then all your activity (watch history) will be associated with that account and the app id. Even if you logout later, the app and everything you watch after will always be associated with the google account you logged in with. Turning off history tracking in your account doesn't stop this.
If you have logged into any google account from any other device (with app, or just with browser) without a vpn then those accounts get associated with your ip address. Any other access to any google service from that ip will automatically get associated with any previous google accounts used from that ip address. Slowly all your devices and account become known and associated together.
Specially bad if you have other devices in your home that have google stuff embeded in them (like other android phones). In that case the location of those devices is known and ip is known and all past and future activity to google where your ip or device is known will all be associated with your identity.
One cant erase the past, but if you use a google free phone (gos) and also hide your ip, then you can stop future tracking on that particular device (as long as you dont login).
This is why its a good idea to use libretube or newpipe. Know that libretube hides your ip from google. But newpipe doesnt.
Im tired of typing. Good luck.