use last_common as start in BlockFetcher

[eval-exec]

What problem does this PR solve?

Issue Number: close #xxx

Problem Summary:

What is changed and how it works?

Proposal: xxx

What's Changed:

Related changes

• PR to update owner/repo:
• Need to cherry-pick to the release branch

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No code ci-runs-only: [ quick_checks,linters ]

Side effects

• Performance regression
• Breaking backward compatibility

Release note

None: Exclude this PR from the release note.
Title Only: Include only the PR title in the release note.
Note: Add a note under the PR title in the release note.