index: Move last_locator_write_time and logging to end of threadsync loop

Summary:
This avoids having commit print a needless error message during init.

Co-authored-by: furszy <mfurszy@protonmail.com>

This is a backport of core#29671
Depends on D17703

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, roqqit

Reviewed By: #bitcoin_abc, roqqit

Differential Revision: https://reviews.bitcoinabc.org/D17704