Hashed Storage: Only set as `read_only` when starting the per-project migration

What does this MR do?

This change improves the way we flag a project as read_only during the Hashed Storage migration. Instead of flagging it early when scheduling the migration, we flag only when we need to migrate. This is essential for big installations like gitlab-dot-com where the entire migration can take several hours or days.

What are the relevant issue numbers?

• part of !23955 (merged)
• gitlab-com/gl-infra/infrastructure#4869

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• Tests added for this feature/bug
• Tested in all supported browsers
• Conforms to the code review guidelines
• Conforms to the merge request performance guidelines
• Conforms to the style guides
• Conforms to the database guides
• Link to e2e tests MR added if this MR has Requires e2e tests label. See the Test Planning Process.
• Security reports checked/validated by reviewer