Aside from the manual way to detect your data being stolen and used for identity compromising activities, have some tools that i may share you the link on requests where you can detect datas amd documents that are already being misused by identity thefts.
But sure, what one need to do is to minimise how many sites you do kyc on and try to stick to reputable services and sont follow offers that promises high returns but ask for your documents.
Are you talking about haveibeenpwned? As long as you check every single one of your email addresses, then perhaps you can accurately detect if your personal details have been leaked. My old address had been leaked quite a few times, and unfortunately, once your details are out in the darknet, they remain there forever. Unfortunately, we can't predict if we're going to be a victim of a data leak, as many websites may end up hacked/exploited, but it's always best to avoid KYC documents when possible.
Casinos are deemed quite safe, because they're dealing with huge sums of money, but nothing is guaranteed and may happen at any time.