I use the Aeotec multi sensor 6 to do just that, I even use the same Lutron switch. The multi sensor 6 also has a motion sensor so I use that to control the lights. BTW there's a slick little community app called "Bathroom Humidity Fan" that is extremely useful and does exactly what you are looking to do.
I use to have that setup. I changed for 3 reasons:
I set the level differently if the house is dry, mostly in the winter, (setup a higher humidity level) or if it is already humid, mostly in the summer. Also, in the winter I like to avoid exhausting air that I have spent $ to heat...
I have an air exchange system that I turn on first, in good part because it includes a heat exchange so avoids losing my heated air. If the humidity reaches a second, higher threshold, I will then turn on the bathroom fan.
The fan never seemed to turn on... The humidity sensing switch I had couldn’t be configured, and would pretty much never turn on.
Always best to have a reference humidity somewhere in the house far from the bathroom. I have a sensor downstairs in our living room, and the bathroom humidity is compared against that.
I use two rules. I've tried many times to create a single RM 4.0 rule and it has never worked properly. This is created with RM 3.0, but you should be able to do it with two separate RM 4.0 rules. If you can get it to work in a single rule, knock yourself out! I gave up after trying many times with many different iterations.
Mind me asking what humidity sensor that is? I assume Xiaomi/Aqara?
I ask because it is reporting the humidity value as a decimal, which in another thread we were reminded by Bruce that they shouldn't do that (integer only). Humidity reporting as a decimal will break simple automation and basic rules (at least until the next hotfix release).