They aren't as far as I can tell.

On one hand, it's safer they only hold money for a day or two.

On the other hand, no FDIC insurance. If Stripe (or Visa or Mastercard) were to poof, what would actually happen to in-flight money? Seems like you could pretty easily lose a day or two where the client got charged, and it never got paid out.

It's not Stripe or Visa "going poof" that would be an issue it would the underlying banks they use that add risk. Stripe/Visa are not FTX. Payment processors don't use in-flight transactions to pay liabilities (salaries, rent, etc.). They also don't (as far as I'm aware) convert that cash into other assets like bonds.

However, the money may be stored in a money market account i.e short term bonds or even if it's a more normal savings account the bank itself depends on fractional lending and bonds.

I'm be very surprised if any major payment processor hasn't vetted the institutions that hold transaction funds. That said some payroll companies were hit by SVB's collapse but more so on not being able to accept checks than loosing already received funds.

The payment processor I worked for ran routine capitalization audits on the partner banks they used.

It’s a mix. Payment processors holds user funds in fbo accounts at partner banks.

Fbo accounts are technically the banks, the processor keeps the records of whose funds are whose within the account and the fdic limit applies to the beneficiary (the person the processor is holding the funds for).

Source: I worked for the treasury group at a payment processor.