I’ve been there. I ended up buying an ASUS-RTAX53U, flashed it with OpenWRT, since it supports VLANs. You have full control over your device. For switches I’m using zyxel 8 port managed ones. Having 4 ssids, Im satisfied, and can be done pretty cheap. If you want to get started check OneMarcFifty’s tutorials.

Can be a lot of things. For my parents problem was the old lan card in pc, which was 10/100. Can be router port, switch port, cable. How do you measure it? Can you plug ur pc directly to the modem or router?

Mesh or wireless bridge?

Consider buying something that supports openwrt. I currently use Asus RT-AX53U, it is cheap, wifi 6 compatible, and if you want you can use openwrt, which you can use to create a mesh, or just fast roaming access points. If you dont want to mess around with itj ust now, you can still use the asus aimesh. I had an existing mesh, but I wanted vlans for my iot devices, and I had to replace some of my devices.

802.11r was what I needed, which is fast roaming (thats what they call ethernet backhaul) Mesh is 802.11s. You might need both, but you can combine it

I use it for my homelab, its been perfect do far

Even if your port is forearded, make sure 8096 is allowed through the firewall of your computer. Also make sure you are not behind a cgnat if you want to access it externally.