Out-of-sample queries on fitted and loaded models (newdata across predict/do/ate, compile caching)

[daimon-pymclabs]

In a production setting a fitted (or loaded, see #507) model is queried repeatedly on new data. Today that path is uneven:

• predictions() / comparisons() / slopes() accept newdata=, but predict(), do(), ate() and friends do not. Out-of-sample predict() relies on the user calling pm.set_data() themselves.
• Panel models with lag() / adstock() bake n_units / n_times into the scan graph, so scoring a new panel shape means building a new model.
• Each query compiles PyTensor functions from scratch, so cold-start latency is high for a service answering many small requests.

Proposal

• A consistent newdata= argument (business units, validated per Data contracts: validate new data against the training schema and add an explicit missing-data policy #512) across predict, do, ate/att/atu/cate, and prob.
• A documented route for scoring new panel units / horizons (e.g. forecasting forward from the last observed state).
• Cache compiled posterior-predictive / intervention functions on the model so repeated queries with the same shape skip recompilation, plus an explicit warmup() hook for services.
• Optional: a thin serializable query/result layer (dict or JSON in, dict or JSON out) that a service wrapper can call directly.

Part of #509 (production readiness).