Address all formatting warnings from linters

[hcho3]

• Fix all warnings from pre-commit.
• Exclude whitespace checks from cpplint. Let clang-format handle whitespace formatting.

I used the AI assistance to resolve many of the cpplint warnings.

Tips for the reviewer: Make sure to hide whitespaces when reviewing. I will split this PR into smaller PRs, once pre-commit run --all-files passes without any warning.

[trivialfis]

Oh ...

[hcho3]

Note: JNI files and C API demos have been excluded from cpplint checks.

[hcho3]

Note: Some checks in cpplint have been turned off.

[hcho3]

Turning this to draft for now. I didn't realize that #11953 would uncover this many formatting issues ...

[hcho3]

TODOs

• Resolve all compilation errors. Clang-format reordered #include's and uncovered many missing headers in the process. For example, src/common/probability_distribution.h fails to include <xgboost/base.h> for the XGBOOST_DEVICE macro.
• Run pre-commit run --all-files in the CI.
• Turn off more checks to make the necessary change size smaller.
• Split off this PR into smaller PRs, each PR containing at most 20 files.

[trivialfis]

I suggest we fix the headers first using #11790

• It doesn't override the main code logic. We can handle header changes.
• It's actually not trivial. I tried. Useful to get it out of the way as the first step.

[RAMitchell]

Lets not do it this way :) I didn't intend anyone to run pre-commit run --all-files (yet). The changes should happen slowly only on changed files. Lets keep the exclusions you discovered and otherwise try to work one commit at a time.

The main problem I see right now is that we are running one of our python lint scripts in pre-commit which touches every file - it should be split into its component tools in the pre-commit script and run only on changed files.