Cold starts are fine, starts right up and sounds normal. Idle's at about 700-800 rpm after a cold start in the summer and then drops to about 600 rpm after it warms.

on a cold engine uncap the radiator, start it up, there should be no bubbles. if there are it's a sign that the head gasket is blown and coolant is being lost into the combustion chamber of the engine instead of going around it to keep the engine cool.

overheating usually causes blown head gaskets.

Internal leakage symptoms can be quite subtle: one or two cylinders missing for just a few seconds after a cold (overnight) start.

I ask because you say there's no external leakage yet the reservoir is emptying. A gross internal leak should be detectable via Doctorbee's method. A small internal leak might require a leakdown test to detect e.g., pressurizing each cylinder at top-dead-center and looking for water pushing back through the radiator cap.

Rad caps are cheap, replace or test if you haven't already.

From there, bleed and fill the system. Start the car and let it run (ac off) - of course check the temp gauge every now and then. Give everything a good look over once the car gets to op temp. You are trying to find a leak and there are plenty of places it could be coming from. Yes it could be a head gasket but I'm hoping for something else........when was the timing belt/water pump last done - weep hole on the wp?