[services] Backup - Move reactors' implementations to source files

Summary:
Depends on D3779

https://linear.app/comm/issue/ENG-917/try-to-move-reactors-implementations-to-cpp-files

Moving reactors' implementations to the source files.

Test Plan:

cd services
yarn run-backup-server

Reviewers: palys-swm, jimpo, ashoat

Reviewed By: palys-swm

Subscribers: jimpo, ashoat, palys-swm, Adrian, atul, benschac, yayabosh

Differential Revision: https://phabricator.ashoat.com/D3780