[MSD benchmark] fix data race in GetWebAssets

[khaliqgant]

MSD benchmark PR recreated from Martian Code Review Bench.

Source PR: grafana#90939
Dataset: grafana
Original title: fix data race in GetWebAssets

What is this feature?

Small fix to a data race when accessing shared global state holding web assets.

Why do we need this feature?

[Add a description of the problem the feature is trying to solve.]

Who is this feature for?

Everyone.

Which issue(s) does this PR fix?:

None

Special notes for your reviewer:

Please check that:

• It works as expected from a user's perspective.
• If this is a pre-GA feature, it is behind a feature toggle.
• The docs are updated, and if this is a notable improvement, it's added to our What's New doc.