Add variance-budget and scale-invariant fit training diagnostics

[bwengals]

Adds training diagnostics that describe how a GP splits the response variance across the mean function, the GP signal, and the observation noise, plus a scale-invariant likelihood-based "excess fit" metric for both VFE and the exact GP.

Motivation

excess_fit_per_n was sensitive to the mean and scale of y: the GP defaults to a zero mean function and y enters the fit uncentered, and the metric referenced sigma**2, so the log-determinant's scale dependence was not cancelled. Its documented "goes to 0 at the noise floor" was also wrong (it sat at -0.5).

What's added

• variance_budget(gp, X, y) (model-agnostic): decomposes the response variance into mean / GP-signal / noise via the law of total variance, Var(y) = Var(m(X)) + mean(diag(K)) + mean(sigma(X)**2). Returns the three contributions, their fractions (sum to 1), and var_ratio = total / Var(y) for calibration. Invariant to the mean and scale of y; works for any mean function, composed (sum) kernels, and scalar or heteroskedastic sigma.
• vfe_diagnostics: gains the four budget fields, and excess_fit_per_n is redefined to fit_per_n + 0.5*log(2*pi*Var(y - m(X))) + 0.5. Referencing the residual variance instead of sigma**2 cancels the log-determinant's scale term, so the metric is scale-invariant and reads 0 against a constant-mean Gaussian.
• unapproximated_diagnostics(gp, X, y) (new): the exact-GP analogue, built on marginal_log_likelihood. Reports mll/fit/logdet, per-point fit and complexity, the same scale-invariant excess_fit_per_n, and the variance budget.

All new fields flow through compile_scipy_diagnostics, tracked_minimize, and to_idata automatically via the namedtuple plumbing.

Heteroskedastic sigma

Every metric handles sigma as a scalar or an X-dependent length-N vector (sigma * ones(N) then mean(sigma**2)).

Related

Relates to #7 (live training monitor dashboard): each new namedtuple field is a ready-to-plot series. Does not close any open issue.

Test plan

• pytest tests/ 275 passed
• pre-commit run --all-files clean (runs on every commit)
• scripts/run_mypy.py 37/37 pass

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📚 Documentation preview 📚: https://ptgp--40.org.readthedocs.build/en/40/

[bwengals]

Merging with two known-infra check failures, unrelated to this PR:

• windows / py3.12: the unpinned test env currently resolves a broken conda-forge MinGW toolchain (g++ 16.2.0, ld.exe: cannot find dllcrt2.o), so pytensor cannot compile its C backend and every C-dependent test fails. Reproduced on a freshly built env after purging the Actions caches; main would fail identically today.
• build and inspect the package: the pinned build-and-inspect action bundles a twine that predates Metadata-Version 2.5.

The PR-relevant signal is green: ubuntu py3.13, mypy, pre-commit, docs, plus the full suite locally on the rebased head (276 passed, mypy 38/38). A CI-fix PR for both issues follows.