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GH-31521: [C++][Flight] Migrate Flight SQL client to Result (#36559)

### Rationale for this change

Arrow introduced a `Result` return object that can be used in place of passing output parameters. Most of Flight has already been migrated. 

### Are these changes tested?

C++ tests pass, which involve the sqlite and acero example servers. Any other testing we would like to see?

```
100% tests passed, 0 tests failed out of 84

Label Time Summary:
arrow-tests         = 168.18 sec*proc (35 tests)
arrow_acero         = 106.32 sec*proc (12 tests)
arrow_compute       =  76.46 sec*proc (13 tests)
arrow_dataset       =  78.09 sec*proc (12 tests)
arrow_flight        = 123.81 sec*proc (2 tests)
arrow_flight_sql    =  19.29 sec*proc (1 test)
filesystem          =  10.39 sec*proc (2 tests)
parquet-tests       =  55.24 sec*proc (9 tests)
unittest            = 627.40 sec*proc (84 tests)

Total Test time (real) = 120.83 sec
```

### Are there any user-facing changes?

Yes. The protected methods DoPut, DoGet, and DoAction for the SQL client have been updated. DoGet already exposed a public API and that has been updated to be virtual.
* Closes: #31521

Authored-by: Dane Pitkin <dane@voltrondata.com>
Signed-off-by: David Li <li.davidm96@gmail.com>