COVID-19 contact tracing API stats? Is there a way to see how many unique contact tracing IDs my phone has registered via BLE?
Nope.
As part of the joint Apple/Google initiative, a great deal of emphasis is placed on the privacy of the data. Authorized Covid-19 Exposure Notification Apps are the only ones that can use the API. Even the Apps themselves have no way of asking such a question.
On Android the Google Play Service is the one sending out identifiers and recording nearby identifiers.
From Architecture section of the documentation:
https://developers.google.com/android/exposure-notifications/exposure-notifications-api
Google Play Services:

Manages daily random keys
Manages Bluetooth broadcast and collection
Identifies whether the user was in close contact with a confirmed case
Presents permission requests to user for scanning/reading beacons and submitting user keys on diagnosis.

The Exposure Notification App submits a set of suspect identifiers (presumably from a secure medical source, i.e. those who have tested positive) into the Google Play Service API and that returns a risk score on that identifier.
You as a user won't know anything beyond what the app will tell you and the app is limited to the data in ExposureSummary/ExposureInformation or ExposureWindow as found in the Exposure Notification API data structure documentation. Wether all of the detail in available in exposure datasets is presented to the user is determined by the App authors presumably in conjunction with local health authorities.