Public companies file public records, so yes, it is public.
And First Republic Bank looks like it could be the next to fail, likely within days, barring intervention. Without a systemic backstop the runs will almost certainly continue
The stock price has nothing to do with whether the bank is solvent. It's about the balance sheet and if they can service a large amount of withdrawals within a short timespan.
Stock price can only be treated as an indicator of what the market thinks.
And First Republic Bank looks like it could be the next to fail, likely within days, barring intervention. Without a systemic backstop the runs will almost certainly continue