Would be interesting to find out the reason: Bluetooth on the HA server hence is irrelevant for this path, so anything related to that should not affect whether the voice assistant speaker works or not.
And it is indeed a HA-internal dependency. The error is emitted here: core/homeassistant/components/config/config_entries.py at 20f40a1d7c7b67def111f6aa86bd43f2f21f181b · home-assistant/core · GitHub
Probably a bootstrapping issue, with some of its Python dependencies missing: core/homeassistant/components/bluetooth/manifest.json at 20f40a1d7c7b67def111f6aa86bd43f2f21f181b · home-assistant/core · GitHub
HAOS comes with all dependencies for all (bundled) integrations pre-installed, while on DietPi, the HA core installation pulls only the core dependencies. So when an integration is added, HA installs their additional dependencies, as defined in above manifest (for the “bluetooth” component) on demand. But this does not always succeed, as there are sometimes dependency cycles, which do not appear to HA developers, since they focus on the all pre-installed HAOS.
If you want to debug it with the DietPi HA installation, the service logs should reveal some related error:
journalctl -u home-assistant