As you may know I use a Google Wifi (now called Nest Wifi) at home for my router. Google Wifi is a managed router meaning the security updates are handled by Google. Other managed routers are, eero, Orbi, Asus ZenWiFi AX, TP Link Deco and many others.
Just like you can access the controls of tour router via you phone from anywhere so can techs at those companies. Technically they could view any non-encrypted traffic on the network plus view any shared files via Samba (network file sharing protocol). If you are paranoid maybe this type of router is not for you, but you just might be missing out. The automatic updates protect your router from any exploits that might be discovered and the remote management it really great for the elderly or the less technically inclined.