The technical pilot of Edit Suggestion Counts stored in Linked Artifacts cache (backed by Headless VE) will only enable suggestion counts for a deterministic sample of pages.
T433024: Implement sampling requirements for Headless VE technical pilot will determine the sample proportion.
Once that is decided, we should pre-warm / backfill these suggestions for the latest revision of the pages in the sample.
Since sampling is determined in VisualEditor edit check PHP code, a PHP maintenance script that iterates through all page_ids and 'warms' the cache for pages in sample would probably suffice.
The code recently added for T432733: Server Side Edit Suggestions - Linked Artifacts Cache precompute job could be factored out into a callable function from a MW Service.