For example, take https://github.com/python/cpython/pulls, notice that the tab says 2.2K, while the overview only lists only 1154 open. Half of the open pull requests simply cannot be found with the search, which is the API used on that page.

These PRs still exist, but the only way to open the page is if you happen to know the PR number, or if you push to a branch, which seems to trigger the PR to get reindexed in search.