refactor: enforce strict backend typing

Enable strict TypeScript and reject non-null and definite-assignment assertions. Declare externally populated DTO fields, preserve runtime validation, and narrow values at their owners.

Verified: backend verify (257 tests), unchanged OpenAPI, and 21 SQLite/HTTP tests on retry. The initial SQLite run had two timeouts; baseline HEAD passed 21 tests as well.

src/common/decorators/api-safe-error-response.decorator.ts

@@ -8,10 +8,10 @@ import {
 
 export class ProblemDetailsDto {
   @ApiProperty({ example: 401 })
-  status: number;
+  declare status: number;
 
   @ApiProperty({ example: 'UNAUTHORIZED' })
-  code: string;
+  declare code: string;
 
   @ApiProperty({
     required: false,