How do you get people to pay through your website?

Don't let anyone communicate with each other directly and restrict all personally identifiable information so they can't find each other outisde of your website.

Easier said than done, but at least we have examples of this kind dynamic already.

AirBnb - they offer ways of getting refunded if someone doesnt hold their end of the deal.
so it's safer to transact with them.

Freelance websites - they go for the restrictive communication outlined above, from what i've heard, harsh punishment for not following their communication rules.
It's not a particulary good look for a "marketplace" kind of business in my opinion.

but all of these kinds of business survive cause they provide accountability, that dealing with a person directly wouldn't, but providing that "accountability" i.e refunds and stuff, can be a costly business to maintain.