Can I charge my iPhone 15 with a 30-watt charger...and is this affecting my iPhone 15's battery health??

No Problem at all. The iPhone charging system automatically takes as much wattage as it is designed for. The output of the charger doesn’t mean anything.

Best Buy associate advised me that I needed to buy a new charger cube for my iPhone 15 pro. Said the lower watt cubes that I had used for my SE and 11 would cause battery to heat up, resulting in damage/shortened life. True?

You were outright lied to by an incompetent Best Buy drone.

Absolute rubbish. I wouldn't trust anything a Best Buy employee says.

I was told the same thing today by a Verizon rep

Generally, the sales floor is not the place to go for accurate information. Remember that the folks at the stores make nothing if you don't sell you something.

They do make a buck or two if they can sell you a new power adapter or other accessory.

You could use a 100 watt power adapter if you wanted to.

You are welcome to believe whomever you want to.