Hi @Andy ,
From the error in the ULS log, it seems to be only related to search database. As all sites cannot access, please check if there is any other error in the ULS log.
Besides, according to your description, we can do some troubleshooting.
First, check to see whether your SQL Server still works, make sure all SQL server services are running.
Ping SQL server from SharePoint server and see if you get the response.
Second, ensure that TCP\IP and Named Protocols are enabled for the local SharePoint instance.
Go to SQL Server configuration Manager, and check whether Shared Memory option is enabled under "Client Protocols". It should be enabled.
Third, clear the SharePoint Configuration Cache files and restart the timer. Please click here for your reference.
Note: Microsoft is providing this information as a convenience to you. The sites are not controlled by Microsoft. Microsoft cannot make any representations regarding the quality, safety, or suitability of any software or information found there. Please make sure that you completely understand the risk before retrieving any suggestions from the above link.
Fourth, ensure the port number 1433 is open (on the server where you are hosting the SQL databases). If you are using a custom port, please enable the port number for incoming connections in the firewall. Please click here for your reference.
Finally, check the Event Viewer log to see if there is any error message.
Thanks,
Yanli Jiang
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