It's a good question - Stripe's Stablecoin Account documentation is good reference here (they denominate balances in USDB, one of these "custom stablecoins" from Bridge): https://docs.stripe.com/crypto/stablecoin-financial-accounts...
"It’s always backed one-to-one by the equivalent value of US dollars held in cash and short-duration money market funds at BlackRock."
So while there are other (potentially novel) sorts of counterparty risks - the backing is definitely more robust than (and pretty much entirely decoupled from) Bitcoin/the rest of the crypto sphere, and is closer to dropping funds off in a Fidelity money market.
Another good (early - 2023) read on this topic: "There are now two types of PayPal dollars, and one is better than the other " https://www.moneyness.ca/2023/09/there-are-now-two-types-of-...