How to connect SQL Server back to .NET project

To give a bit of context, I was assigned to be a maintainer for a website developed with .NET framework, we lost contact with previous developer. That said, I'm a bit new to the .NET world and will need a bit of time to adapt, one thing is left to figure out how to connect the SQL Server database back to the project (it is hosted locally on the company server), and I still don't know what SQL Server type they are using.

I tried locating some clues in the web.config file but didn't come to any conclusion:

<entityFramework>
    <defaultConnectionFactory type="System.Data.Entity.Infrastructure.LocalDbConnectionFactory, EntityFramework">
        <parameters>
            <parameter value="mssqllocaldb" />
        </parameters>
    </defaultConnectionFactory>
    <providers>
        <provider invariantName="System.Data.SqlClient" 
                  type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer" />
    </providers>
</entityFramework>

Also in the web.config i have the following (removed information for security reasons):

  <connectionStrings>
    <add name="" connectionString="data source=MSI;initial catalog=MelkiDBbranch1;user id=;password=;MultipleActiveResultSets=True;App=EntityFramework" providerName="System.Data.SqlClient" />
  </connectionStrings>

Along with a really long Entity Framework file which is SQL related, I will access the local server soon but I need to have a general idea on what I should look for in order to establish the connection on my PC

We have this connection string:

data source=MSI;initial catalog=MelkiDBbranch1;user id=;password=;MultipleActiveResultSets=True;App=EntityFramework

This connection string tells us the server name is MSI, and the database name on that server is MelkiDBbranch1 (since one server can host many databases). I expect the user id and password are redacted, and you can see actual values in the real string.

To connect to this server you need to make sure the MSI name resolves on your network (there's probably a default dns suffix). If you're using SQL Server Management Studio, you can then connect to a database engine using the MSI name for the server, with SQL Server Authentication selected and using the login/password from the connection string.

If you expand the "Options" section there should also be a place to choose the database, but this is optional.

Finally, depending on the network and firewall configurations, you can probably do this with Management Studio installed on your own computer, without needing to first login to the server.