Run check_syntax as pre-commit hook

[Lestropie]

Felt the itch to give this a try, and Claude seems to have done a functional job of it.

I tried adding a second commit that contained code that would violate check_syntax. The pre-commit hook rejected it. It was clear from the response time that check_syntax was only executing against the git diff and not the entire codebase. So might be a useful one to drag in just to cut back on pluralistic commits.

Closes #3301.

[Lestropie]

There is a mild risk in this approach:

check_syntax performs many of its checks based on a modified text file where newlines have been replaced by whitespace, so the code per file is just one long line. This is to catch erroneous usage where the offending code crosses one or more newlines.

In this "diff" mode however, the input will be a concatenation of all newly added lines.
This means that:

• If the interaction between a new line if code and the surrounding code violates a rule, it won't be caught, ie. false negative.
• If two lines of code that are separated, but sequential once only newly added lines are considered, manage to combine together to violate a rule, that would be a false positive.

I think these are decreasingly likely to occur, but it's imperfect nonetheless.

Possible strategies:

• Have check_syntax analyse not only any added lines, but also however many surrounding lines are typically included in a git diff.
• Have check_syntax introduce some kind of "barrier" in the code it generates from the git diff, so that the regexes can't get any hits based on merging added lines and skipping existing lines between them.

[github-actions]

clang-tidy review says "All clean, LGTM! 👍"