Move common logging GetArgs code to init/common

Summary:
This is a partial backport of core#21732
https://github.com/bitcoin/bitcoin/pull/21732/commits/1fb7fcfa52569a652d3ea55c210b725e60b7d86f

Depends on D12561

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D12562