I literally quoted the conversion time, it’s right in the datasheet.
Yes, it would be nice if they said what happens if you ignore the rule, and better guidance on how to avoid that.
But my point is, this: it looks like the conversion wait is deterministic, so if you keep track of the elapsed time, then you know whether a conversion is imminent. Basically, the 64s counter starts when the thing is first powered up. (i.e. when it thinks the time is 00:00:00.)
Suppose you power it up (so it’s “blank”). Then right before you write the current time (let’s say 14:00:00) to it, you read out the saved time and it says 00:00:23 (so 23s have elapsed since power up.) You now know that the next automatic conversion will be at 14:00:41. (14:00:00 + 64s - 23s). And then again at 14:01:45, 14:02:49, and so on. That gives you a huge window of time.
If you don’t know when it powered up, then you poll the heck out of the BSY until it is high, and you’ve got your reference datum. You don’t need to do that again, just once.
In all cases, the 64s elapsed time should be checked by reading it from the RTC, not from your MCU’s system clock that might drift.
As for when the conversion takes place during the second: well wouldn’t that be pretty easy to test? Power it up, don’t set the time, and at 00:01:03, poll the time and BSY registers furiously, and correlate the time changeover to the BSY state.