The best way to correctly fight Shadow IT is to provide equipment and services so good nobody would even care using something else.
Some people will always want to bring their own equipment, but a lot of it is caused by penny pinching or lack of options
It quickly grows past the 2-3 sanctioned models. Everyone wants something not on the list, lots of bickering of "why was that model chosen?", etc. Well that pre-approved model is $150, this is only $175. Bob got that $175 model, this is only $200, it's not that much. Jenny got that $200 model, this is only $250. Jenny's got a $250 keyboard? I gotta upgrade, here's this $300 model... Wait did the company just buy Bill a 55" 4K display? I need that too...
Suddenly your $150/person budget has exploded to replace everyone's equipment for $1,000+ otherwise it's just not fair someone else got more.
Personally I'm fine with me buying and owning my own kb+m. Maybe give a once a year or two office hardware stipend or whatever. Then otherwise make basic stuff available for free. If you're wanting a $200 keyboard you're probably wanting a particular $200 keyboard, and it's probably not one of those 2-3 approved models.
Wired connections are inherently more difficult to attack. In security critical applications banning bluetooth is perfectly reasonable.
[1] https://www.youtube.com/watch?v=GRJ7i2J_Y80
[2] https://www.youtube.com/watch?v=EksyCO0DzYs