[CodeHealth] Clean web_contents() in SitePerProcessHitTestBrowserTest

This is a no-op change to utilize the helper method `web_contents()`
in this test, mostly to replace `shell()->web_contents()`.

Change-Id: Ie119d737f26c7034c5ec2fb2fafaaafc244ead76
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6603453
Commit-Queue: Mustaq Ahmed <mustaq@chromium.org>
Reviewed-by: Alex Moshchuk <alexmos@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1467509}