The recursive-submodule check was unreachable: a preceding `[[ url != ... ]] && echo`
inside a `cmd | while` block caused the pipeline to exit 1 on the last iteration
when all URLs were valid, and `set -e` aborted the script before reaching the
recursive check. The recursive check itself also only echoed without exiting.

Switch each loop to `while ... done < <(cmd)` and replace the `&&` shorthand
with `if ...; then echo; exit 1; fi` so the first violation is reported and
exits 1, as intended.

The Style check job did not opt into the submodule cache, so submodule
working trees were never populated. With no `contrib/<x>/.gitmodules`
present, the recursive-submodule check silently passed even when a
submodule pulled in nested submodules (as `contrib/silk` did).

Two changes:

- Opt `style_check` into `needs_submodules=True` so the cache is restored
  before the job runs.
- Fail the script up front if any registered submodule has no `.git`
  gitlink file. Using `[ -e "$path/.git" ]` is ~250x faster than parsing
  `git submodule status` and is the exact signal we need.

The submodule cache restores .git/modules but does not check out the
working trees, so check_submodules.sh would fail with "Submodule X is
not initialized". Run `git submodule update --init` first.

Reading .gitmodules from the bare repo's HEAD trusted that HEAD always
matches the superproject's gitlink, which can drift if the bare repo
gets touched out-of-band. Resolve every submodule's pinned SHA from the
superproject up front with a single `git ls-tree HEAD`, then read
.gitmodules at that exact SHA from each bare repo.

Addresses review feedback on PR ClickHouse#105053.

`git show $sha:.gitmodules | grep -q ...` returns grep's exit code, so a
missing pinned commit (incomplete/corrupted cache) silently looked like
"no nested submodules". Add an explicit `git cat-file -e` check so a
missing commit fails loudly.

Addresses review feedback on PR ClickHouse#105053.

The check verifies `.gitmodules` (no recursive submodules, valid URLs,
name == path). It requires submodules to be initialized, which made the
style check ~20s slower because it had to download the submodule cache.
Move it to the arm_tidy build, which already initializes submodules.

Addresses ClickHouse#105053 (comment)