What is a decent, not too pricey hardware option if I want to do extend a WLAN (with WPA2 enterprise as client)?

I would like to optimize the Wifi-Connection in one of the dorm rooms. One of the back rooms has bad Wifi reception. So I would like to install a WLAN extender in the front room. However the WLAN is using WPA2 Enterprise (I.e. not using PSK, but user/password combination). Off-the-shelf repeaters seem to not support WPA2 enterprise.

So I think of buying a router, install OpenWrt and have my own private network in my back room. I read that this is possible with no problems using OpenWrt - I probably need to learn the configuration details when I have the router device here. (I managed to use OpenWrt on a cheap TP-Link WR841 earlier for a simple AP configuration bridging all ports (WLAN+LAN), so avoiding a subnet for WLAN)

I have no clue, if there are any hardware features I should look out for! Especially whether the creation of a new, second network (my private one) while at the same time beeing a client on the primary network has any special implications.

Therefore I would be grateful for advise. I think I don't have special needs in terms of performance. Should of course  be decent and it should be possible to browse and stream. But I'm a single user with few devices. Price range 50-100 € would be fine.

What devices would be Ok options for doing WLAN extensions?