Hi. I’m doing a similar thing but I purchased a Galaxy S10 that had a broken screen but the touch screen is working from eBay for $60. This does everything up to the highest end emulation on android (GC, Wii, PS2 and 3ds). I’m using this as my hub and I also have another usb 2 port plugged into this. I’m using a 100w USBC power charger to power everything because I also have a couple of external USB3 drives plugged into the hub. And I’m using a PS4 controller to play games. Works natively as a mouse as well. I also have 2.4ghz keyboard mouse combo plugged into the USB2 hub as well if needed and a second controller that is 2.4ghz as well Here’s a complete rundown I typed for someone else.. That all being said I have my game room/office upstairs. I can stream PS5/Xbox One and PC to my phone downstairs too. With my PS I am testing software now. I’m trying Moonlight and Parsec. The neat thing is my pc can handle PS3 and Switch emulation so I can stream everything to my phone downstairs. It’s an awesome setup for about $120 all in.
Don't laugh but I use this guy: https://www.amazon.com/dp/B07H2ZS1B5/ref=cm_sw_r_cp_apa_i_Jd5cFb00CAA4J
At the time this was $37 🙈
This exceeds your price point, but offers Ethernet, 3 USB 3.0, HDMI, and USB-C passthrough. Bought several.
https://www.amazon.com/dp/B07H2ZS1B5/ref=cm_sw_r_cp_apa_i_Fk6cFbGK2MKQ5 this one right here