blockstorage: [refactor] Use chainman reference where possible

Summary:
This is a backport of core#21575 [5/6]
https://github.com/bitcoin/bitcoin/pull/21575/commits/fa121b628d51bb0e25eb3fbd716881fa55527dc7

Depends on D11350

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Subscribers: Fabien

Differential Revision: https://reviews.bitcoinabc.org/D11351