Since you did not provide any information about this in your question, I assume that you have the credentials in your connection string.
From a security point of view, you should try to avoid this, if possible, use Windows authentication. Obviously, this requires that you have access to the Active Directory environment, and all servers are deployed in it.
If not, it is always better to block the web server, and not try to make sure that the files on the disk are protected from unauthorized access by different users.
Even if this is not possible, I will follow the approach given by the other answers, encrypting confidential content using DPAPI.
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