How to identify which common terminal of the 3-way switch is connected the hot wire
Turn off breaker. Disconnect wires. Connect appropriate meter (safely). Turn on breaker, look at meter. If no voltage, turn off breaker, move to other switch, connect meter, repeat.
Or use a test lamp, if you are old-fangled. The folks around here are fond of &quot;non-contact voltage testers&quot; but they appear to be prone to confusing results. I'm old-fangled enough to prefer a meter, but not old-fangled enough to prefer a test lamp.
If your switches were actually wired &quot;that way&quot; you'd have a neutral connection in one box, and none in the other box. But things are often less clear-cut than that in practice - can't hurt to look for it, though.