gh-149377: update bundled pip to 26.1.1

[sbidoul]

• Issue: Update bundled pip to 26.1.1 #149377

[miss-islington-app]

Thanks @sbidoul for the PR, and @hugovk for merging it 🌮🎉.. I'm working now to backport this PR to: 3.13, 3.14.
🐍🍒⛏🤖

[bedevere-app]

GH-149379 is a backport of this pull request to the 3.14 branch.

[bedevere-app]

GH-149380 is a backport of this pull request to the 3.13 branch.

[bedevere-bot]

⚠️⚠️⚠️ Buildbot failure ⚠️⚠️⚠️

Hi! The buildbot AMD64 Debian root 3.13 (tier-1) has failed when building commit 9f9a273.

What do you need to do:

1. Don't panic.
2. Check the buildbot page in the devguide if you don't know what the buildbots are or how they work.
3. Go to the page of the buildbot that failed (https://buildbot.python.org/#/builders/1441/builds/1935) and take a look at the build logs.
4. Check if the failure is related to this commit (9f9a273) or if it is a false positive.
5. If the failure is related to this commit, please, reflect that on the issue and make a new Pull Request with a fix.

You can take a look at the buildbot page here:

https://buildbot.python.org/#/builders/1441/builds/1935

Summary of the results of the build (if available):

==

Click to see traceback logs

Traceback (most recent call last):
  File "/root/buildarea/3.13.angelico-debian-amd64/build/Lib/test/support/__init__.py", line 856, in gc_collect
    gc.collect()
ResourceWarning: unclosed file <_io.FileIO name=11 mode='wb' closefd=True>


Traceback (most recent call last):
  File "/root/buildarea/3.13.angelico-debian-amd64/build/Lib/test/support/__init__.py", line 856, in gc_collect
    gc.collect()
ResourceWarning: unclosed file <_io.FileIO name=13 mode='wb' closefd=True>