[Bug]: Flat File Importer - Support for non-master

### Description

Same issue as #21647

When running the file importer on a database that you are connected to via a user that does not have access to master.

Error message:
```javascript
Error running command mssql.flatFileImport: Microsoft.Data.SqlClient.SqlException (0x80131904): The server principal "DatabaseNameThatIsNotMaster" is not able to access the database "master" under the current security context.
Cannot open database "master" requested by the login. The login failed.
Login failed for user 'DatabaseNameThatIsNotMaster'.
at Microsoft.Data.SqlClient.SqlInternalConnection.OnError(SqlException exception, Boolean breakConnection, Action`1 wrapCloseInAction)
at Microsoft.Data.SqlClient.TdsParser.ThrowExceptionAndWarning(TdsParserStateObject stateObj, SqlCommand command, Boolean callerHasConnectionLock, Boolean asyncClose)
at Microsoft.Data.SqlClient.TdsParser.TryRun(RunBehavior runBehavior, SqlCommand cmdHandler, SqlDataReader dataStream, BulkCopySimpleResultSet bulkCopyHandler, TdsParserStateObject stateObj, Boolean& dataReady)
at Microsoft.Data.SqlClient.TdsParser.Run(RunBehavior runBehavior, SqlCommand cmdHandler, SqlDataReader dataStream, BulkCopySimpleResultSet bulkCopyHandler, TdsParserStateObject stateObj)
at Microsoft.Data.SqlClient.SqlInternalConnectionTds.CompleteLogin(Boolean enlistOK)
at Microsoft.Data.SqlClient.SqlInternalConnectionTds.AttemptOneLogin(ServerInfo serverInfo, String newPassword, SecureString newSecurePassword, TimeoutTimer timeout, Boolean withFailover)
at Microsoft.Data.SqlClient.SqlInternalConnectionTds.LoginNoFailover(ServerInfo serverInfo, String newPassword, SecureString newSecurePassword, Boolean redirectedUserInstance, SqlConnectionString connectionOptions, SqlCredential credential, TimeoutTimer timeout)
at Microsoft.Data.SqlClient.SqlInternalConnectionTds.OpenLoginEnlist(TimeoutTimer timeout, SqlConnectionString connectionOptions, SqlCredential credential, String newPassword, SecureString newSecurePassword, Boolean redirectedUserInstance)
at Microsoft.Data.SqlClient.SqlInternalConnectionTds..ctor(DbConnectionPoolIdentity identity, SqlConnectionString connectionOptions, SqlCredential credential, Object providerInfo, String newPassword, SecureString newSecurePassword, Boolean redirectedUserInstance, SqlConnectionString userConnectionOptions, SessionData reconnectSessionData, Boolean applyTransientFaultHandling, String accessToken, IDbConnectionPool pool, Func`3 accessTokenCallback)
at Microsoft.Data.SqlClient.SqlConnectionFactory.CreateConnection(DbConnectionOptions options, DbConnectionPoolKey poolKey, DbConnectionPoolGroupProviderInfo poolGroupProviderInfo, IDbConnectionPool pool, DbConnection owningConnection, DbConnectionOptions userOptions)
at Microsoft.Data.ProviderBase.DbConnectionFactory.CreateNonPooledConnection(DbConnection owningConnection, DbConnectionPoolGroup poolGroup, DbConnectionOptions userOptions)
at Microsoft.Data.ProviderBase.DbConnectionFactory.TryGetConnection(DbConnection owningConnection, TaskCompletionSource`1 retry, DbConnectionOptions userOptions, DbConnectionInternal oldConnection, DbConnectionInternal& connection)
at Microsoft.Data.ProviderBase.DbConnectionInternal.TryOpenConnectionInternal(DbConnection outerConnection, DbConnectionFactory connectionFactory, TaskCompletionSource`1 retry, DbConnectionOptions userOptions)
at Microsoft.Data.ProviderBase.DbConnectionClosed.TryOpenConnection(DbConnection outerConnection, DbConnectionFactory connectionFactory, TaskCompletionSource`1 retry, DbConnectionOptions userOptions)
at Microsoft.Data.SqlClient.SqlConnection.TryOpen(TaskCompletionSource`1 retry, SqlConnectionOverrides overrides)
at Microsoft.Data.SqlClient.SqlConnection.Open(SqlConnectionOverrides overrides)
at Microsoft.SqlTools.ServiceLayer.Connection.ReliableConnection.ReliableSqlConnection.b__30_0() in /_/src/Microsoft.SqlTools.ManagedBatchParser/ReliableConnection/ReliableSqlConnection.cs:line 316
at Microsoft.SqlTools.ServiceLayer.Connection.ReliableConnection.RetryPolicy.<>c__DisplayClass25_0.b__0(RetryState _) in /_/src/Microsoft.SqlTools.ManagedBatchParser/ReliableConnection/RetryPolicy.cs:line 128
at Microsoft.SqlTools.ServiceLayer.Connection.ReliableConnection.RetryPolicy.<>c__DisplayClass26_0.b__0(RetryState retryState) in /_/src/Microsoft.SqlTools.ManagedBatchParser/ReliableConnection/RetryPolicy.cs:line 141
at Microsoft.SqlTools.ServiceLayer.Connection.ReliableConnection.RetryPolicy.ExecuteAction[R](Func`2 func, Nullable`1 token) in /_/src/Microsoft.SqlTools.ManagedBatchParser/ReliableConnection/RetryPolicy.cs:line 179
at Microsoft.SqlTools.ServiceLayer.Connection.ReliableConnection.RetryPolicy.ExecuteAction(Action`1 action, Nullable`1 token) in /_/src/Microsoft.SqlTools.ManagedBatchParser/ReliableConnection/RetryPolicy.cs:line 138
at Microsoft.SqlTools.ServiceLayer.Connection.ReliableConnection.RetryPolicy.ExecuteAction(Action action, Nullable`1 token) in /_/src/Microsoft.SqlTools.ManagedBatchParser/ReliableConnection/RetryPolicy.cs:line 127
at Microsoft.SqlTools.ServiceLayer.Connection.ReliableConnection.ReliableSqlConnection.Open() in /_/src/Microsoft.SqlTools.ManagedBatchParser/ReliableConnection/ReliableSqlConnection.cs:line 312
at Microsoft.SqlTools.ServiceLayer.Connection.ListDatabaseRequestHandler`1.GetResults(ISqlConnectionFactory connectionFactory, ConnectionDetails connectionDetails) in /_/src/Microsoft.SqlTools.ServiceLayer/Connection/ListDatabaseRequestHandler.cs:line 111
at Microsoft.SqlTools.ServiceLayer.Connection.ListDatabaseRequestHandler`1.HandleRequest(ISqlConnectionFactory connectionFactory, ConnectionInfo connectionInfo) in /_/src/Microsoft.SqlTools.ServiceLayer/Connection/ListDatabaseRequestHandler.cs:line 81
at Microsoft.SqlTools.ServiceLayer.Connection.ConnectionService.ListDatabases(ListDatabasesParams listDatabasesParams) in /_/src/Microsoft.SqlTools.ServiceLayer/Connection/ConnectionService.cs:line 1113
at Microsoft.SqlTools.ServiceLayer.Connection.ConnectionService.<>c__DisplayClass96_0.<b__0>d.MoveNext() in /_/src/Microsoft.SqlTools.ServiceLayer/Connection/ConnectionService.cs:line 1362
ClientConnectionId:a4f25640-3e4b-4245-b29c-5d5c718faa11
Error Number:916,State:2,Class:14. This is likely caused by the extension that contributes mssql.flatFileImport.
```

### Steps to Reproduce

Connected to database via SQL Login authentication type, database name specified, user does not have access to master.

Everything works fine, but when trying to run the data importer / flat file importer, it produces the above error message after several seconds have passed, presumably It's attempting to connect to master during those few seconds.

To replicate I imagine you would need to set up a database user that is restricted to only that database and then try to use that with the file importer.

### Affected Area

- [ ] Connection dialog (SQL Server | Azure browse/Fabric browse)
- [ ] Query editor
- [ ] Query results panel
- [ ] Object Explorer
- [ ] GitHub Copilot integration
- [ ] Preview/Edit data
- [ ] Table Designer
- [ ] Schema Designer
- [ ] Schema Compare
- [ ] Local SQL Server Container provisioning
- [ ] SQL database in Fabric provisioning
- [ ] DACPAC/BACPAC export/import
- [ ] SQL Database projects
- [ ] Query Plan Visualizer
- [x] Other (please describe below)

### If you selected "Other", please describe the affected area

mssql.flatFileImport

### Environment Information

Version: 1.117.0
ms-mssql.mssql - 1.42.1
Commit: 10c8e557c8b9f9ed0a87f61f1c9a44bde731c409
Date: 2026-04-21T16:12:14-07:00
Electron: 39.8.7
ElectronBuildId: 13841579
Chromium: 142.0.7444.265
Node.js: 22.22.1
V8: 14.2.231.22-electron.0
OS: Linux x64 6.19.14-arch1-1

### Confirmation

- [x] I have searched existing issues and couldn't find a match
- [ ] I want to work on this issue