Hopefully the actual bill wording doesn’t leave this ambiguous, but I think the intent of “exclusively” here is meaning that they don’t also represent the buyer’s interest (dual agency), not that they have an exclusive deal with the landlord.

No it doesn't mean they can't work with multiple landlords, it means the represent the landlord(s) interests, not the tenants.

If a tenant hires his own agent to find an apartment, that agent would (a) represent the tenant and (b) the tenant would pay for that service.

But I'm not sure what stops the landlords from just raising the rent to cover the broker fees. Unless there's enough competition from landlords who don't use brokers.

Landlords will raise the rent but can only raise the rent to what the market will bear (which presumably they’re doing anyway). They then have incentive to ensure the broker is worth the fee.

Previously landlords would require renters to work with (and pay) the broker, so there was no incentive to choose a cheaper broker.

Here’s the thing: let’s assume that that’s exactly what happens. It’s still a good thing. This is now reflected in the visible part of the cost enabling people to make better decisions.

Renters negotiate the rent with the landlord. They don't negotiate the agent fee. They have to pay it or waste more time searching for another apartment with the risk of another agent charging an unknown and unaffordable fee.

It doesnʻt matter if they raise the rent to cover the fees. As another comment noted, THAT is a major win for price transparency. That would be a big improvement by itself.