Only disable the background responsiveness timer once the process has been suspended. We wait a long time on macOS to suspend background processes so the background responsiveness timer still is useful during this "running in the background" period.
<rdar://111702782>
Pull request: https://github.com/WebKit/WebKit/pull/15747
Committed 265958@main (f008b08e6385): <https://commits.webkit.org/265958@main> Reviewed commits have been landed. Closing PR #15747 and removing active labels.