Because of changes to Shopify's API, it is no longer possible to directly edit the Fulfillment Service field for product variants. Originally, variants could only be stocked with a single fulfillment service, and you could bulk edit that field through the app.
With changes starting in 2022, variants can now be stocked at multiple fulfillment services. As a result, the upcoming version of the Shopify API has removed the ability to modify the Fulfillment Service field.
As a replacement, you can connect or disconnect the variants from specific locations managed by different fulfillment services.
Learn more about connecting and disconnecting inventory locations.