init: start indexes sync earlier

Summary:
The mempool load can take a while, and it is not
needed for the indexes' synchronization.

Also, having the mempool load function call
inside 'blockstorage.cpp' wasn't structurally
correct.

This is a partial backport of core#27607
https://github.com/bitcoin/bitcoin/pull/27607/commits/ed4462cc78afd2065bbf5bd79728852b65b9ad7f

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D17744