If your hardware can handle the extra load, Scrypted is a lot better at this than HA or Homebridge. HA doesn’t even support HKSV. There is an officially supported Add-on to run Scrypted in HA. Scrypted is directly linked to HomeKit.
Camera feeds and full doorbell now load in 0,1-0,2s in HomeKit when running Scrypted on a NUC with an i3-1315U. Home Assistant itself still takes about 1s to load the stream and sometimes black for 1-2secs before picture appears.
Notifications from HomeKit are now faster than from Unifi Protect itself and definitely a lot faster than a HA notification would be.