I am also looking for a way to do this without pulling every order in the store every time i want to run a report.
Topic summary
Ability sought: filter/search Orders by a key/value in customAttributes (aka order_notes in REST) via API.
What’s supported: GraphQL’s OrderConnection allows filtering by fields like email, status, created_at, discount_code, etc., but not customAttributes. The Order object’s customAttributes are not searchable. REST likewise doesn’t support filtering by order_notes.
Official position (earlier reply): Filtering by customAttributes/order_notes is not possible in either REST or GraphQL.
Workarounds: None provided in-thread. One participant asked about Saved Searches; no solution or example was shared. Others note pulling every order to post-filter is impractical.
Recent updates: Multiple follow-ups ask whether this has changed (including by 2023) and request the ability to query by attribute or metafield value. The thread contains no confirmation of new support or changes.
Status: Unresolved/feature gap. Key open question: whether Shopify APIs will add filters for customAttributes or metafields on Orders.