How to use Find Contribution to find folk who Donated via a line item on a Membership Price set
Seems like the old chestnut about storing financial type on contribution, where it originated, vs line item, where it later appeared, leading to the sort of issue you've described. There was talk a while back of retiring financial type on contribution, which would seem to require changing contribution search to check financial type on line items instead, in the way you describe.

You've specified Find Contributions but as a workaround for now, does the Bookkeeping Transactions report provide what's needed?