My smart tv doesn’t run android, it runs a proprietary Sony OS.

With my shield, I can run anything android can run like smart tube, jellyfin, Plex, emulation station, steam in home streaming etc.

This is why android tv boxes exist. Your tv is probably pretty underpowered or doesn’t even run android, this solves those issues to enable you to run pretty much anything you want on your tv.

I’m happy with my TP-Link Omada router. Very capable, super easy to use, feature packed. More than capable for your needs and gives you room to grow to setup more advanced networking