RasPi or old Mac Mini

One or two Bluetooth proxies might improve your Bluetooth coverage - they’re quite cheap, but you have to do a bit of flashing yourself.

They also allow you to play with room presence detection, if you’re interested in that sort of thing.

The standard advice for Zigbee would be to experiment with a few more routers. There isn’t a magic ratio of routers to end devices - it depends entirely on the layout and structure of your house - but the key thing is that messages need a choice of many possible paths. You would expect to see a complex web of connections between routers (the ovals) and a single connection to each end device.

If you haven’t found it already, the Home Assistant Cookbook has an extensive Zigbee section.