How to approach something like this? Learn a few things. I don't think simply upgrading to win11 will solve your problem tbh and you're right to be a bit skeptical of that. Prime b660m k d4 is a budget board so they skimp on the vrms & heatsink and there's nothing you can do to improve the heatsink because it's keyed to the design of the mobo. You could contrive to mount a fan directly over the vrroom vrms but, even if it were cooler it might cause them to draw more power with that cpu than they can in reality handle well.
Or 'effectively' keyed might be a better phrase. Even if you could squeeze some more performance out of them with more cooling they aren't the greatest vrms quality wise so power delivery also matters.
What's you're power supply? Make/Model/Age?
13600k tdp 189w maximum turbo power is very demanding. Not as monstrous as the
13700k 253w maximum turbo power... but still high.
The recently unleashed
13400f dials maximum turbo power back to 148w whilst the
12400f dials it back to 117w.
So essentially wouldn't use that cpu with that board. 13600k is one of the few in the range that overclock well and b660 isn't capable of overclocking there's simply no way to get the best out of the cpu with that board.
What cpu cooler are you using? A
contact frame (and prequel
installation instructions) may also help improve thermals which is something I would use on a budget board and it also helps prevent the cpu warping if you aren't aware of that issue, but could possibly void your warranty since nobody trusts no-one to tie their shoelaces let alone install a cpu in a socket with fragile pins, and torque up the contact frame correctly. It's basically at your own risk. And no warranty with a budget board and a $350 cpu that might be prone to warping isn't a 'budget friendly risk'.
What you're trying to do is hard. I would just use a 12 or 13400f on it might as well since you'll never hit the hi notes of a 13600k anyway it's throttling whether due to thermals or simply poor power delivery, just hope you don't have a bent pin in your socket.
Bent pin in the socket isn't warrantable either it's considered user error and you might only be able to get it fixed for a fee if they even offer a reconditioning service at all. You could to try and bend them back with a needle but if they snap off there's no more moves. Yippeeki-A mobo.
So basically just pay attention to your cooler, power supply and cpu, as well as the quality of the mobo you are using.
Psu tier list
You can't simply slap any combination of components together and expect it to work even if the components fit in the sockets the board has been gimped to fit the 'budget' bracket.
So you have a mid to hi Raptor lake cpu on a lo end board and nothing will improve it's limitations. If you have a quality power supply, good or excessive cooler, and also can successfully install a contact frame it might just operate within it's capability rather than lose a bit of performance from the wonky socket lever and poor cooler contact, besides the lo end vroom vrms.
Expense you go to, to 'maybe' partially remedy the 'budget' board problems might just get you a better mobo anyway. 'Budget' here is pretty much a 'false economy'. You'd need a good cooler/psu any day of the week anyway with any other board and cpu too.
Maybe you could try under volting the cpu but still that's another can of worms that could be problematical and won't remediate a budget board either. b660 kinda sux all around it's one if the limitations of 12/13 gen.
Difference between you and reviewers? You don't have the luxury of benching dozens of boards and cpus that might even have shipped free for marketing and promotion purposes, and gaining experience. You get to buy one board and one cpu - so be judicious about it.