[REQ][DART-DIO] copyWith extension for json_serializable as the serializationLibrary

Is your feature request related to a problem? Please describe.

The default 'built_value' provides a builder pattern to 'rebuild' an object with modified properties. The 'json_serializable' option for the dart-dio generator generates completely frozen classes and in doing so, one has to mutate objects in a cumbersome way like so: final model2 = Model(model1.elem1, model1.elem2 + 1).

Describe the solution you'd like

Dart already leverages a common copyWith pattern to maintain immutability.
copyWithExtension package exists to generate a copyWith in the same part file. So the model classes can be annotated with the @CopyWith() annotation, in addition to the @JsonSerializable() annotation. The generated model/dtos would then have a generated copyWith() method in the same part file as the json_serializable's boilerplate. This would then more closely match the functionality given by default 'built_value' serialization library.

Describe alternatives you've considered

Post generation, I have run the following script to:

1. Add the dependencies to pubspec.yaml
2. Add the @CopyWith() to each class in the models directory
3. Rerun the build_runner

# Annotate every class with `CopyWith`
find lib/src/model -type f -name '*.dart' | while read -r file; do
# Insert import if missing
grep -q "copy_with_extension" "$file" || sed -i '' "/package:json_annotation/a\\
import 'package:copy_with_extension/copy_with_extension.dart';
" "$file"

# Insert @CopyWith() if missing
grep -q "@CopyWith" "$file" || sed -i '' "/@JsonSerializable/i\\
@CopyWith()
" "$file"
done

Additional context

The default 'built_value' already provide a safe way to maintain immutability and this other implementation should atleast match in terms of it

Start with the dart-dio generator's json_serializable model generation and the build_runner setup described in the issue, then inspect how generated model part files and pubspec dependencies are handled. Done means generated models can use copy_with_extension alongside json_serializable, producing copyWith methods while preserving immutable model behavior; add coverage for the generated output.