p2p: Make timeout mockable and type safe, speed up test

Summary:
This is a backport of core#19499 [2/2] and core#23740
https://github.com/bitcoin/bitcoin/pull/19499/commits/fadc0c80ae4e526fb2b503f7cc02f6122aaf1de5

The second PR is a temporary fix for an intermittent failure that will later be reverted in core#23758

Depends on D10964

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Subscribers: Fabien

Differential Revision: https://reviews.bitcoinabc.org/D10965