test: feature_init, only init what's needed per perturbation/deletion round

Summary:
Avoids initializing and syncing components not under test.
This not only speeds up execution a bit but also helps isolate
and debug issues more easily, as logs aren't flooded with
unrelated details.

This is a partial backport of core#32835
https://github.com/bitcoin/bitcoin/pull/32835/commits/abd07cf7332e4e15fa4ac0e756f3610b0c7b4b6f

Depends on D18624

Test Plan: ninja check-functional

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D18625