Put fines for the suppliers in the contract that they have to pay for each violation of contract, ban them from the platform and be public about it. There should also be rules about not handing out direct contact info to the client, only marketplace-supplied business cards.

They will try to be clever about it, but sooner or later it will come out. Often the users don't even they did it and accidentally blow their cover. You can also make test appointments with someone who will report back to you about attempted rule violations, once you have suspicions.

You can also counteract the leakage by setting up analytics about "unusual" canceling customers, which you will then manually contact (which should be part of your anti-churn strategy anyway). E.g. it could be somewhat suspicious that customers stop booking on your platform after they booked a specific supplier once. This is actually a pretty good use-case for ML.

On the more "positive" side, you can try to build a hard to replicate tech solution that helps their workflow but is also so deeply ingrained that circumventing the system becomes more of a hassle.

You will never get to 0% leakage, but there are a few techniques to get close.