[AZ-812] Region API: rename Latitude/Longitude → Lat/Lon (OSM convention)

Mirror of AZ-794 (inventory z/x/y rename). RequestRegionRequest.cs renames C#
props Latitude→Lat / Longitude→Lon and adds [JsonPropertyName("lat"/"lon")] so
the wire format is unambiguous under the AZ-795 strict-parsing stack
(UnmappedMemberHandling.Disallow → legacy {"latitude":..,"longitude":..} now
returns HTTP 400 instead of silently coercing).

Updates all in-repo consumers: API handler (Program.cs), integration tests
(Models.cs, RegionTests.cs, IdempotentPostTests.cs, SecurityTests.cs), the
performance harness (run-performance-tests.sh PT-03/04/05/07), and module
docs (common_dtos.md, api_program.md; system-flows.md F2 already used
lat/lon). New RegionFieldRenameTests.cs covers AC-4 both directions (new
format → 200, legacy format → 400). Smoke green; no regressions.

region-request.md contract doc not bumped here — AZ-808 publishes v1.0.0
directly with the post-rename names per AZ-812 coordination clause.

Batch 01 of cycle 8. PASS_WITH_WARNINGS (one Low DRY finding for follow-up
test-helper consolidation; details in
_docs/03_implementation/reviews/batch_01_cycle8_review.md).

Co-authored-by: Cursor <cursoragent@cursor.com>

SatelliteProvider.Common/DTO/RequestRegionRequest.cs

@@ -1,4 +1,5 @@
 using System.ComponentModel.DataAnnotations;
+using System.Text.Json.Serialization;
 
 namespace SatelliteProvider.Common.DTO;
 
@@ -8,10 +9,12 @@ public record RequestRegionRequest
     public Guid Id { get; set; }
 
     [Required]
-    public double Latitude { get; set; }
+    [JsonPropertyName("lat")]
+    public double Lat { get; set; }
 
     [Required]
-    public double Longitude { get; set; }
+    [JsonPropertyName("lon")]
+    public double Lon { get; set; }
 
     [Required]
     public double SizeMeters { get; set; }