Hello.
How does bluetooth work on the RPI?
If I disable the Wi-Fi connection in HA in the network/WLAN section, will the BLE range be better?
Has anyone rebuilt an RPI with an external antenna?
I don’t think that deactivating the WLAN will improve the Bluetooth range 
And in the description you will find enough dongels with external antennas
Off topic: there are posts on the net that there is interference problems. After 2 years I loved my ssd away from my rpi4 (it was under the pi now 30cm away) and my.eifi went from 40mbit to 80mbit speed.
So maybe it will have impact when you turn it off your wifi…
External antenna can make things worse… I bought a BT dongle with externall antenna and range is weaker than with PCB antenna. The point is that better antenna doesn’t only “see” good signals better but bad ones, too. I’ve had quite bigger noise with external antenna and thus range was smaller.
One of alternative solutions is to place more BT proxy points.
but the solution should then be about the correct placement of the antenna
It would be, sure, if it’s possible. Many times it isn’t… you connect Bt dongle to usb input of HA hardware and antenna is attached directly to BT dongle. If you connect it via cable (to move it away) you loose all advantage on cable losses. So only option is to lead usb extension cable, but again not too long, because then again you loose all advantage (power loss on cable)
Best in class hardware managing the minimal resources for the pi - approach in my opinion is to run headless with an SSD, then just turn off wifi, bluetooth, hdmi, sound and utilize ethernet for performance.