bext: include integration tests snapshots into client Percy build

Created by: taras-yemets

Combines browser extension and web snapshots into a single Percy build.

It was initially added in https://github.com/sourcegraph/sourcegraph/pull/31555/, but then reverted as one of the tests appeared to be flaky. It took some time to fix the browser extension integration tests setup (https://github.com/sourcegraph/sourcegraph/pull/33598), and new changes to how Percy build is finalized were made in https://github.com/sourcegraph/sourcegraph/pull/33498. Re-adding browser extension Percy snapshots to the final Percy build.

Test plan

Check the pipelines on the client code PRs and ensure that Percy pipeline result includes web and browser extension snapshots.