The FDIC take over only happened after the massive amount of withdrawals/bank run the day before. Which is the nuance in the above statements... they had assets, but after selling what they could to meet immediate withdrawal obligations, the assets they had left (HTM) weren't worth as much if sold immediately than their booked value. If the assets could have been held until maturity (HTM), they would have been worth their book value.
So, only after the run did they become insolvent. The change from illiquid to insolvent happened quickly, but without those withdrawals, the illiquidity could have likely been managed to avoid an outright insolvency (probably through a sale).
If it were only illquid, it would be far easier to find a buyer and it would have already been sold by now.
[1] https://dfpi.ca.gov/2023/03/10/california-financial-regulato...