Few observations:
- Do a wifi speed test near your router, and then where your streamer will be to determine whether you need anything to enhance speed (i.e., to get an idea of how much speed you lose with distance).
- A dongle is just a design feature; a Raspberry Pi has wifi capability without the need for a dongle. The three wifi streamers i currently use all have dongles. It’s just how they implement wifi.
- If you need something to enhance speed, I don’t see any reason why your original thought - TP Link with extender - wouldn’t work. I use the mesh system network rather that my router’s network because I have 3 floors and my router is in the basement.
Hope that helps.