Maybe I'll try it again. I wonder if it's worse when it's connected by idle though. Like when you get in the car and it connects and stays connected for the whole journey, is that worse than scanning?Bluetooth uses around 2-15mW on your phone. (source) depending on data transfer rate, sleep mode etc
Assuming a middle value for that on a 10Wh battery (around the size in a non-XL Pixel 1) you'd lose maybe 2.1% of your battery to Bluetooth if you left it on for 24 hours. Almost negligible.