I would say your first attempt is correct. That there will be more than one bank involved.
'Downgrades' in this context is a financial term regarding the credit rating of a bank (people can also have credit ratings). A credit rating is basically an evaluation of how likely it is that a borrower will repay a debt.
If a bank's rating is downgraded, it means a bank will have to pay more money to borrow (higher interest rates) or perhaps be refused a loan, as it will have been deemed less likely to be able to repay the money.
With regards to your second interpretation, if there was only one bank involved then 'banks' would be singular. For example:
'Analysts say that would spook markets, potentially leading to a downgrade of the bank that owns much of the debt, ...'
More likely is that the sentence would mention the single bank by name, '...leading to a downgrade of Barclays, the bank that owns much of the debt...'
Please note I used Barclays only as an example.
Like I said at the start, I'm not a teacher only a native, but I hope I have helped you.
Student or Learner