An assistant connected to Keeper.sh could already read and write events, but not answer the question people actually ask it, which is when you are free.
Finding free time works out the open slots across everything you have connected, over a range you give it. It reads availability rather than counting events: something marked free, or marked as working elsewhere, does not block a slot, while busy and out-of-office do. Give it working hours and working days in a named timezone and "find me an hour on Thursday" stops offering you 6am.
The other two are about control. Syncing on demand clears the backoff on any source that had been backing off after errors and queues a push to every calendar you copy into, throttled to once a minute. Pausing stops a calendar syncing in both directions while leaving it connected and its settings intact. All three work over the REST API as well, so the same actions run from a script.
Read more about everything Keeper.sh does.