Help adding Yale Assure SL deadbolt through Bluetooth

I have a Yale Assure SL deadbolt, with the Yale smart access module and wifi connect. I can control it via Bluetooth from my phone and through the August app. I also have an August Smart Lock Pro Gen 3 with its wifi connect.

I have both locks accessible in Home Assistant through the August integration, but I’d prefer to have a full local control setup instead. I have several devices already set up for local control using HA’s HomeKit imitation and they work great, so I was pretty happy to find out that at least the Yale lock has HomeKit support since it does have the HomeKit logo and code on its smart module. From my understanding that’s only for HomeKit over Bluetooth though. So I bought a couple of ESP32 boards to use as Bluetooth Proxies with the ESPHome firmware. I flashed them and set them up near the locks. After a couple of minutes, the August lock was autodiscovered by HA under the Yale Access Bluetooth integration. I was able to successfully set up the August lock using Yale Access Bluetooth, however, neither than integration nor the HomeKit integration seemed to be able to discover the Yale lock. I did check and my phone doing a Bluetooth scan (using Wifiman app), can easily see the Yale lock’s Bluetooth signal from the location of the ESPHome Bluetooth Proxy’s location just 5 feet away from the lock.

Is there something I’m missing here? From what I’ve read online, adding a Bluetooth Proxy will allow the HomeKit integration to automatically discover Bluetooth HomeKit devices, and at the very least, the Yale lock should be discovered by the Yale Access Bluetooth integration since the August lock was.

Just to make sure I didn’t get a bad ESP32 board, I tried a different one and same result, no Yale lock being discovered by HA.

Yes, I did try searching through the forum for similar posts, but they all seemed to have been created back before 2022, which from my understanding HA had a lot worse Bluetooth support back then, so not necessarily relevant today.