Follow-up
I wanted to provide an update on this issue. After further investigation, I discovered that the root cause was related to how Shopify Functions are registered when using the new Dev Dashboard and shopify app dev workflow.
When functions are registered via the new Dev Platform, they appear in the dashboard and have UUIDs, but they are not actually registered in Shopify’s backend in a way that the Admin API recognizes. This led to the errors I was seeing when trying to save or update rules, including the metafield access errors described above. More here.
Resolution
Switching back to the classic Partner Dashboard and using the classic CLI flow to register and deploy the functions resolved the issue. Once the functions were registered this way, the Admin API recognized them, and all related errors (including the metafield access errors) disappeared—without any code changes.
I hope this helps others who might encounter the same problem. Thanks!