Stage 1: I'd set up both APs with same SSID and password, put them into same subnet and give devices where it matters a static DHCP lease. Do not disable beacons ("hidden AP") or mess with beacon intervals (~10/sec), because devices will otherwise have trouble picking the strongest AP. If a device travels around, like you going from basement into attic with a laptop, it will simply switch to a different AP with stronger signal without you doing anything.
If you live downtown with many APs and got Android F-Droid store, get the very good open source "WiFiAnalyzer" from VREM Software Development to gauge band congestion. Depending on Android version, later versions might throttle wifi scanning to conserve battery. There is a developer menu setting on all but Android 10 I believe where you can turn that throttling off. The app will probably notify you though. If you live more like in the countryside and need 2.4 GHz for devices, look at this graph:
List of WLAN channels - Wikipedia At 40 MHz channel width the entire 2.4 GHz spectrum is basically full with two APs, one at channel 1 and the other at channel 13 (11 for US, then it overlaps already a bit). If you'd put both APs on same channel, with same side-channel, you'd essentially half (or worse... wifi air link is fairy magic) throughput.
Stage 2: Devices might still reset IP connections on re-association, but keeping the DHCP lease static is the best you can do. On Linux there is a systemd-networkd setting called "IgnoreCarrierLoss=" see
systemd.network which allows you to specify say 10 seconds so the IP stack will keep its stuff together and not reset running IP sessions, if you travel between SSIDs and the card in the laptop takes a moment to associate to that other AP.
Stage 3: If you want to go overboard, install a Radius and read up on "IEEE 802.11i/RSN/WPA2 Pre-authentication", e.g. see
en:users:documentation:hostapd [Linux Wireless] This will connect both APs so they will be able to exchange authentication information.
You only want anything meshy if you have no ethernet cable to where a bridge AP lives and you want to extend range beyond the last ethernet connected AP. In that case a small directional antenna for the uplink part will be advisable depending on AP-AP distance.
Or, see what you can achieve with a directional antenna on that one AP. There's a metric ton of simple to build but highly efficient antenna designs out there on the web, search for wifi antenna + (yagi,biquad,dual loop,cantenna). Might even get away with a larger stacked dipole. But keep the cable short and high quality, with low loss at f=2.4 GHz at or below 0.5 dB/meter.