docs: restore macro-free worked problems on functional-api.md (E7)

[ocots]

What

Campaign phase E7 — resolves the one content regression the E6 attic audit (.reports/campaign/N-attics-audit.md, finding F1 / recommendation R2) found: the documentation rewrite kept only the energy double integrator worked in functional (macro-free) form, while the other core gallery problems survived in @def form only. docs/attic/manual-macro-free.md was their only macro-free home, and it is slated for deletion in E6.

Changes

• docs/src/modelling/functional-api.md — "A worked example…" becomes ## Worked problems with seven ### subsections in gallery order: energy (full treatment kept), time, control-free, control-and-variable, turnpike, singular, state-constraint. Each new one: setup block → side-by-side @def / functional model (responsive-columns-40-60, per the Phase-J decision against code-group tabs) → one solve + objective/variable check → links to its examples/* page and the gallery. turnpike is included beyond the audit's six for gallery parity (it post-dates the attic; it is the purest scalar-convention demo). State-constraint uses a nonlinear :path constraint to match its example page (the attic used a box :state bound).
• docs/src-literate/guided-tour.jl — its functional block used u[1] / 0.5*u[1]^2 and a !!! warning claiming callbacks are "always vector-valued", contradicting functional-api.md §"Shapes in callbacks" and the "1-D is a scalar" rule. Fixed to bare scalars; warning rewritten.
• docs/src/modelling/without-control.md — one sentence pointing at the new side-by-side control-free problem.

No change to the public API, Project.toml, or make.jl.

Verification

julia --project=. docs/make.jl builds clean locally:

• all seven subsections' @example blocks execute; the printed objective: macro = …, functional = … pairs are identical for every problem (energy 6, time 2, control-free λ≈0.496, control+variable 0.0387, turnpike 0.375, singular 1.150, state-constraint 7.692).
• guided tour regenerated and built.
• the only "cannot resolve" errors are the six pre-existing @extref items (Plots.plot(::CTModels…) ×4, CTBase.Strategies.parameter ×2), unchanged from main and in the tolerated warnonly classes. No new unresolved @ref.

This unblocks E6 (delete docs/attic/, close the cahier). Audit items F3 (get_strategy_registry double mention) and F4 (193/203 symbol count) are deferred to the E6 §12 walk.

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