Write a safe migration for this change

Changing a schema that live code is already reading and writing.

I need to make the schema change described below against a live database.

Produce:
1. The sequence of deploys required for zero downtime, stating for each step what the application code must tolerate. Assume old and new code run simultaneously during rollout.
2. The forward migration SQL, and the rollback for each step, or a plain statement that a step is irreversible.
3. Locking behaviour: which statements take a lock, of what kind, and how long at my row count. Flag anything that blocks writes.
4. Backfill strategy for existing rows: batched, resumable, and with the batch size stated.
5. What to verify between steps before proceeding.

If the change cannot be done safely as described, say so and propose the closest safe alternative.

Change I need:
Current schema:
Approximate row count:
Database and version:

Schema and data quality. Designing tables, migrating them without breaking live code, and cleaning what you have been handed.