BUG: Fix issue #66552

[jas20han-tech]

• closes BUG: datetimelike arithmetic landing on the NaT sentinel silently returns NaT #66552
• Tests added and passed if fixing a bug or adding a new feature
  - test_arithmetic_landing_on_nat_sentinel_raises (pandas/tests/scalar/timestamp/test_arithmetic.py)
  - test_td_add_sub_landing_on_nat_sentinel_raises, test_td_mul_div_landing_on_nat_sentinel_raises (pandas/tests/scalar/timedelta/test_arithmetic.py)
  - test_dti_add_dateoffset_landing_on_nat_sentinel_raises (pandas/tests/arithmetic/test_datetime64.py)
  - test_tdi_sub_landing_on_nat_sentinel_raises (pandas/tests/arithmetic/test_timedelta64.py)
  - test_implementation_limits updated (pandas/tests/scalar/timedelta/test_timedelta.py)
  - Verified: all 6 fail on un-fixed source, pass with fix; full gate 21524 passed / 724 skipped / 47 xfailed / 0 failed
• All code checks passed.
  - pre-commit run --files <15 changed files>: all hooks pass (ruff, isort, cython-lint, vulture, codespell, whatsnew sort, etc.)
• Added type annotations to new arguments/methods/functions.
  - add_overflowsafe(left, right, raise_on_sentinel: bool = ...) annotated in pandas/_libs/tslibs/np_datetime.pyi; internal Cython cdef helpers (_add_timedelta_overflowsafe) are module-private and need no stubs.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.
  - doc/source/whatsnew/v3.1.0.rst (Datetimelike section, line 363, sorted): datetimelike arithmetic landing exactly on the NaT sentinel now raises instead of returning NaT/wrapping (:issue:66552)
• I have reviewed and followed all the contribution guidelines
• If I used AI to develop this pull request, I prompted it to follow AGENTS.md.
  - AI (opencode, model big-pickle) developed the fix and ran the full 9-step validation checklist; pandas AGENTS.md was loaded and followed throughout.