Update the serialization process

[isofer]

PyMC-Marketing have a list of known failures (see below), and
the codebase uses at least four different serialization patterns with no unified
contract, making it difficult for users to create custom serializable components.

Current Serialization Patterns (4+, inconsistent)

1. to_dict()/from_dict() + register_deserialization — adstock, saturation, HSGP, fourier, events/Basis
2. Pydantic model_dump()/model_validate() — HSGPKwargs, Scaling, LinearTrend, MuEffect subclasses
3. singledispatch serializers — per-type handlers for MuEffects in multidimensional.py
4. Manual JSON encoding — create_idata_attrs() / attrs_to_init_kwargs() on MMM

Design doc (still WIP): https://github.com/pymc-labs/pymc-marketing/blob/isofer/2379-update-serialization-process/docs/plans/2026-03-05-serialization-overhaul-design.md

[github-actions]

Potential Duplicate Issues

• Build out HSGP serialization #2087: Build out HSGP serialization - Directly overlaps with the serialization overhaul; HSGP serialization is one of the four patterns mentioned in the issue.
• Lack of idata.attrs serialization for MuEffects #1921: Lack of idata.attrs serialization for MuEffects - Directly related to the singledispatch/manual JSON encoding patterns mentioned for MuEffects serialization.
• Remove unneccessary attrs serialization #880: Remove unnecessary attrs serialization - Related to the manual JSON encoding pattern (create_idata_attrs() / attrs_to_init_kwargs()) mentioned in the issue.
• LogNormalPrior DeserializableError with build_mmm_from_yaml #2071: LogNormalPrior DeserializableError with build_mmm_from_yaml - A known serialization failure that this overhaul aims to fix.
• Cannot save/load model #1457: Cannot save/load model - Broad save/load issue that the unified serialization contract would address.
• Explore save / load strategy using pickled pytensor graphs #1789: Explore save / load strategy using pickled pytensor graphs - Alternative serialization strategy exploration that overlaps with this overhaul.
• Show off the to_dict and from_dict structure for our classes #1664: Show off the to_dict and from_dict structure for our classes - Directly relates to formalizing the to_dict/from_dict contract that is central to this issue.
• Allow for flexible default in idata attrs creation #877: Allow for flexible default in idata attrs creation - Related to the manual JSON encoding pattern in create_idata_attrs().

[juanitorduz]

@isofer can you pass these issues ⏫ to the plan (https://github.com/pymc-labs/pymc-marketing/blob/isofer/2379-update-serialization-process/docs/plans/2026-03-05-serialization-overhaul-design.md) to ensure we are covering edge and known cases :) (If you have not already)