As a homeowner, your guess is probably correct, can’t confirm without physically being there. Flip them all off and wire it up, turn them back on.
As an electrician homeowner, I’d just swap it live, probably dealing with maybe 16VAC, not enough to shock you. Just tape up (and label) the ends as you remove them from the old thermostat’s mounting plate to isolate them from each other… then install them back down one by one to the new plate.
As an electrician, meter them out to verify what voltage you have at the thermostat and monitor them as you turn off each breaker. You might be able to wire them live.
Those look correct. If you have an outside condensing unit with a disconnect switch it should be off. Most 24V transformers are in the condensing unit. This is what powers the thermostat.
Be careful! You are probably correct, but… if you trip those wires you it won’t shock you and you won’t know right away but can blow a fuse in your system. So yes, test the wires and be sure everything is truly off.