Then split it, that’s what I’d do as a first project too.
The 4 mains-powered temperature sensors: ESP32 on Wi-Fi, straight to Hermetry over MQTT. No gateway, nothing in between, every sensor is a device you can see connect and disconnect. It’s the shortest path and you learn the topics and payloads on something that’s easy to debug.
The 4 battery door contacts: not Wi-Fi. An ESP32 waking up, joining Wi-Fi and doing a TLS handshake for every door open eats AA cells in weeks. Buy ready-made Zigbee contact sensors (a couple of years on a coin cell), a Zigbee USB coordinator, and run a small bridge on a Pi that reports them as child devices of a gateway. More moving parts, so do it second, once the Wi-Fi ones work.
Emily’s not wrong about the mesh, but with 4 battery contacts there’s no mesh to speak of, battery end devices don’t route. Mains-powered Zigbee devices do.
There’s a decent overview of which way to connect what in the docs, it’s basically this reasoning as a table: Choose how to connect your devices.