There have been times where the AirPods Max have sort of crashed, and I cannot get them to connect properly. I find that forgetting the AirPods in the phone/computer and then resetting them by holding down the button allows them to start fresh with a new state. Maybe that can help resolve the issue for you. But Im constantly switching them between three nearby devices so maybe thats why I have this problem. Just throwing it out there in case you haven't tried a reset.
I know I have had this issue and did not have it after reset. Though I do have another annoying, and seemingly unique issue: sometimes, when adjusting the position of the headphone, they do a “click” (and a loud one), and just shut down. After a few seconds, they boot up again.
The farthest from the last reset, the more often it happens. I have no idea why.
I'd suggest experimenting by disabling both and trying to repro. Then re-enabling the features one at a time.
I've never triggered it on the Pro by merely speaking loudly, but they're earbuds and farther from my mouth. What does trigger it for me reliably, is sneezing.