[3.13] gh-120888: Bump bundled pip to 24.1.1 (GH-120889) (#121080)

gh-120888: Bump bundled pip to 24.1.1 (GH-120889)
(cherry picked from commit 4999e0bda091826fcdf303dd439364e1d303a5ce)

Co-authored-by: Pradyun Gedam <pradyunsg@gmail.com>
Co-authored-by: Pradyun Gedam <pradyunsg@users.noreply.github.com>
Co-authored-by: blurb-it[bot] <43283697+blurb-it[bot]@users.noreply.github.com>
Co-authored-by: Hugo van Kemenade <1324225+hugovk@users.noreply.github.com>
Co-authored-by: Alyssa Coghlan <ncoghlan@gmail.com>