Update inventory doc (Azure#52898)

Author: live1206

doc/GeneratorMigration/Library_Inventory.md

@@ -4,9 +4,9 @@
 
 - Total libraries: 414
 - Management Plane (Swagger): 165
-- Management Plane (TSP-Old): 50
+- Management Plane (TSP-Old): 49
 - Management Plane (TypeSpec - @azure-typespec/http-client-csharp): 0
-- Management Plane (TypeSpec - @azure-typespec/http-client-csharp-mgmt): 9
+- Management Plane (TypeSpec - @azure-typespec/http-client-csharp-mgmt): 10
 - Management Plane (TypeSpec - @typespec/http-client-csharp): 0
 - Management Plane (TypeSpec - Unknown TypeSpec Generator: eng/emitter-package.json): 0
 - Data Plane (Swagger): 115
@@ -212,7 +212,7 @@ Total: 115
 
 ## Management Plane Libraries using TypeSpec (@azure-typespec/http-client-csharp-mgmt)
 
-TypeSpec with @azure-typespec/http-client-csharp-mgmt generator is detected by the presence of a tsp-location.yaml file with an emitterPackageJsonPath value referencing @azure-typespec/http-client-csharp-mgmt, or through special handling for specific libraries. Total: 9
+TypeSpec with @azure-typespec/http-client-csharp-mgmt generator is detected by the presence of a tsp-location.yaml file with an emitterPackageJsonPath value referencing @azure-typespec/http-client-csharp-mgmt, or through special handling for specific libraries. Total: 10
 
 | Service | Library | Path |
 | ------- | ------- | ---- |
@@ -230,7 +230,7 @@ TypeSpec with @azure-typespec/http-client-csharp-mgmt generator is detected by t
 
 ## Management Plane Libraries using TypeSpec (Old Generator)
 
-TypeSpec with old generator is detected by the presence of a tsp-location.yaml file without an emitterPackageJsonPath value, tspconfig.yaml file, tsp directory, or *.tsp files. Total: 50
+TypeSpec with old generator is detected by the presence of a tsp-location.yaml file without an emitterPackageJsonPath value, tspconfig.yaml file, tsp directory, or *.tsp files. Total: 49
 
 | Service | Library | Path |
 | ------- | ------- | ---- |