[services] Rust Integration - Catch std::exception in base write reactor

Summary:
Depends on D5025

Linear task: https://linear.app/comm/issue/ENG-1727/catch-stdexception-in-base-reactors

We started using rust, and we use functions that return Result. That Result is then converted into a std::exception in c++ when it returns Err. All over the place in the reactors we handle std::runtime_errors but we should go higher in the hierarchy and catch std::exceptions.

Test Plan:

cd services
yarn run-integration-tests backup

Works as before (of course, you have to start backup and blob services first).

Reviewers: jon, tomek, max

Reviewed By: tomek

Subscribers: ashoat, tomek, atul, abosh

Differential Revision: https://phab.comm.dev/D5026