Improve performance of default auth

[bdraco]

followup to #8966

Calling .origin() is a bit expensive #7583 (comment)

We should probably cache self._base_url.origin() as self._base_url_origin` so we don't have to build it every time

Probably could guard this with self._default_auth being set as well

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.59%. Comparing base (c1dc794) to head (a0c7402).
Report is 3 commits behind head on master.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #9466   +/-   ##
=======================================
  Coverage   98.59%   98.59%           
=======================================
  Files         105      105           
  Lines       35089    35091    +2     
  Branches     4178     4178           
=======================================
+ Hits        34595    34597    +2     
  Misses        329      329           
  Partials      165      165           

Flag	Coverage Δ
CI-GHA	98.47% <100.00%> (+<0.01%)	⬆️
OS-Linux	98.14% <100.00%> (+<0.01%)	⬆️
OS-Windows	96.53% <ø> (ø)
OS-macOS	97.83% <100.00%> (+<0.01%)	⬆️
Py-3.10.11	97.70% <100.00%> (+<0.01%)	⬆️
Py-3.10.15	97.63% <100.00%> (+<0.01%)	⬆️
Py-3.11.10	97.71% <100.00%> (+<0.01%)	⬆️
Py-3.11.9	97.78% <100.00%> (-0.02%)	⬇️
Py-3.12.7	98.19% <100.00%> (+<0.01%)	⬆️
Py-3.13.0	98.17% <100.00%> (+<0.01%)	⬆️
Py-3.9.13	97.60% <100.00%> (+<0.01%)	⬆️
Py-3.9.20	97.53% <100.00%> (+<0.01%)	⬆️
Py-pypy7.3.16	97.16% <100.00%> (+<0.01%)	⬆️
VM-macos	97.83% <100.00%> (+<0.01%)	⬆️
VM-ubuntu	98.14% <100.00%> (+<0.01%)	⬆️
VM-windows	96.53% <ø> (ø)

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[patchback]

Backport to 3.11: 💔 cherry-picking failed — conflicts found

❌ Failed to cleanly apply 03851d1 on top of patchback/backports/3.11/03851d1353f66b4b40593a03c7d5f14b16122944/pr-9466

Backporting merged PR #9466 into master

1. Ensure you have a local repo clone of your fork. Unless you cloned it
   from the upstream, this would be your origin remote.
2. Make sure you have an upstream repo added as a remote too. In these
   instructions you'll refer to it by the name upstream. If you don't
   have it, here's how you can add it:

   $ git remote add upstream https://github.com/aio-libs/aiohttp.git

3. Ensure you have the latest copy of upstream and prepare a branch
   that will hold the backported code:

   $ git fetch upstream
   $ git checkout -b patchback/backports/3.11/03851d1353f66b4b40593a03c7d5f14b16122944/pr-9466 upstream/3.11

4. Now, cherry-pick PR Improve performance of default auth #9466 contents into that branch:

   $ git cherry-pick -x 03851d1353f66b4b40593a03c7d5f14b16122944

   If it'll yell at you with something like fatal: Commit 03851d1353f66b4b40593a03c7d5f14b16122944 is a merge but no -m option was given., add -m 1 as follows instead:

   $ git cherry-pick -m1 -x 03851d1353f66b4b40593a03c7d5f14b16122944

5. At this point, you'll probably encounter some merge conflicts. You must
   resolve them in to preserve the patch from PR Improve performance of default auth #9466 as close to the
   original as possible.
6. Push this branch to your fork on GitHub:

   $ git push origin patchback/backports/3.11/03851d1353f66b4b40593a03c7d5f14b16122944/pr-9466

7. Create a PR, ensure that the CI is green. If it's not — update it so that
   the tests and any other checks pass. This is it!
   Now relax and wait for the maintainers to process your pull request
   when they have some cycles to do reviews. Don't worry — they'll tell you if
   any improvements are necessary when the time comes!

🤖 @patchback
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