Fix ensemble tutorial routing and trajectory access

[ChrisRackauckas-Claude]

Change

Use a scalar prototype and public context-based problem routing for the ensemble tutorial, supply trajectory counts explicitly, and access trajectories through sol.u. Add executable assertions for successful return codes, trajectory count, saved times, initial values, and finite values in the first ensemble solve. Model equations and optimization settings are unchanged.

Failing before / passing after

The same assertions and environment were used on the unfixed page and the corrected page. The diagnostic runner evaluates the actual named example blocks in order:

$ julia --startup-file=no --project=EasyModelAnalysis-ensemble-current/docs reproduce-ema-ensemble.jl .validation/ensemble-current-before-assertions.md full
ERROR: LoadError: TaskFailedException
nested task error: MethodError: no method matching init(::Vector{SciMLBase.ODEProblem{...}}, ::Nothing; saveat::Int64)
[exit 1; type arguments abbreviated]

$ julia --startup-file=no --project=EasyModelAnalysis-ensemble-current/docs reproduce-ema-ensemble.jl EasyModelAnalysis-ensemble-current/docs/src/tutorials/ensemble_modeling.md full
ENSEMBLE_BASE_PASS blocks=20 trajectories=3
[exit 0]

Local native QA: 23/23; Core: 31/31 (basics 9, ensemble 1, examples 4, precompile 1, sensitivity 4, threshold 12), exit 0. An isolated strict Documenter build executed all 20 blocks and rendered 12 plots; exit 0. Scoped Runic 1.10.0 checking included fenced Julia, not just Markdown.

Full strict docs did not pass: exit 124 at six hours, with 33 failed example blocks outside this tutorial (Carcione 4, SEIRHD 2, Petri 2, scenario2 4, scenario3 14, scenario4 7). A later full-context diagnostic also timed out at six hours. An isolated page pass does not replace that gate.

Prior art: #299.

Validation scope

Historical results below were run locally with Julia 1.11.9 before rebasing onto current main (which now includes #336 and #337). The changed page is preserved by the rebase. These are not claims that the full documentation or all downstream packages pass. The user requested draft publication with these outstanding gates disclosed.

Native test/build commands, with a workspace-local TMPDIR and headless plotting:

GROUP=QA julia --startup-file=no --project=. -e 'using Pkg; Pkg.test()'
GROUP=Core julia --startup-file=no --project=. -e 'using Pkg; Pkg.test()'
GKSwstype=100 timeout 21600 julia --startup-file=no --project=docs docs/make.jl

GPU paths, downstream packages, and deployment were not verified. No tests or documentation errors were disabled.

Please ignore this draft until reviewed by @ChrisRackauckas.

The post-rebase page is byte-identical to its locally validated pre-rebase version. Fresh post-rebase QA and focused page checks were launched on September 12 and remain pending at publication; they are not counted as passes. Post-rebase spelling and diff checks passed.

🤖 Generated with Codex CLI 0.153.4 (model: gpt-6-astra; session: local session ID 01a0598f-11b9-72d1-91d9-b2fbb186557d).