[lib/web] fix error handling indirection

Summary: I didn't correctly address the feedback in D11675 + D11676 for the error handling misdirection. This diff should correctly address that feedback + fix the other cases in the codebase that followed this patern

Test Plan: flow + went over the use cases in identity-service-client-wrapper w/ @varun irl to confirm nothing would break

Reviewers: atul, varun, ashoat

Reviewed By: varun, ashoat

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D11689