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GH-40553: [C#] Avoid logger instantiations per request (#40554)



### What changes are included in this PR?

- Replacing `CreateLogger<FlightSqlServer>` with `CreateLogger(typeof(FlightSqlServer))`

### Are these changes tested?

It is not gonna change any behavior 

### Are there any user-facing changes?

No

* GitHub Issue: #40553

Authored-by: Ali Khalili <ali.khalili@truelayer.com>
Signed-off-by: Curt Hagenlocher <curt@hagenlocher.org>