Single mesh node vs. something else for a bedroom dead zone (w/ existing Ethernet)?

Hey everyone, first time posting here. I’m slightly familiar with tech but definitely not a networking pro, so I could use some advice.

I recently moved into a ~1000 sq ft 1-bedroom apartment. The fiber comes into a central telecom box near the front door, which then feeds into the ISP router in the living room. The Wi-Fi in the living room is great, but the signal in the bedroom is honestly terrible; it's a total dead zone for my phone and laptop.

The apartment actually has Ethernet sockets in the walls. I’ve been tinkering with the telecom box and managed to bridge the connection so that the wall port in the bedroom is now live.

Now I'm trying to figure out the best way to actually get Wi-Fi into the bedroom.

My questions:

• Can I just buy a single mesh node (looking at something like a TP-Link Deco X55), plug it into that bedroom Ethernet port, and call it a day?

• If I set the node to Access Point mode, will my devices actually "roam" between the living room and bedroom, or will they just stay stuck to the weak living room signal until it completely drops?

• Is there a more budget-friendly way to do this that I’m missing?

TL;DR

1000 sq ft apartment with a dead zone in the bedroom. I have a live Ethernet port in the bedroom wall. Should I just get a single mesh node to plug in there, or is there a better way to extend the Wi-Fi while keeping the setup clean?

Thank you!