Move common logging AddArg code to init/common

Summary:
This is a partial backport of core#21732 and core#21060
https://github.com/bitcoin/bitcoin/pull/21732/commits/90469c16906ab451bb1250df5e51563870a7ef3b

Depends on D12560

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Subscribers: Fabien

Differential Revision: https://reviews.bitcoinabc.org/D12561