[codex] add elm_ui and terminal_ui example targets

[pcharbon70]

What changed

• add elm_ui and terminal_ui support to mix example.start
• wire the shared example launcher and example docs/specs to advertise the new runtime targets
• add the needed runtime deps across the example apps and resync the generated example READMEs
• align root AGENTS.md with the current .spec workspace guidance
• fix example module ordering and runtime delegation issues uncovered while enabling the new launcher paths

Why

The example launcher and shared tooling only supported the browser live_ui baseline and desktop_ui, so there was no supported path for running a specific example against elm_ui or terminal_ui. While wiring those targets through, a few generated example/runtime issues surfaced and needed to be corrected so the launcher and smoke paths stayed coherent.

Impact

• mix example.start --target-package terminal_ui --backend-mode tty now works for example apps and prints a terminal runtime snapshot
• mix example.start --target-package elm_ui now works as a compatibility/diagnostic path and emits a structured compatibility report when a surface is not directly renderable by the Elm renderer
• mix examples.launch --runtime elm_ui|terminal_ui --dry-run now reflects the new launcher contract
• examples docs, root agent guidance, and .spec/specs/examples/* now match the current runtime-selection behavior

Validation

• cd examples/button && mix example.start --target-package terminal_ui --backend-mode tty
• cd examples/button && mix example.start --target-package elm_ui
• cd examples/shared && mix test test/mix/tasks/examples_tasks_test.exs
• cd examples/shared && mix test test/unified_examples/phoenix_runtime_test.exs

Notes

• Existing desktop_ui unresolved-reference warnings and live_ui HEEx warnings are still present in the workspace.
• I did not include the unrelated local .tool-versions change or untracked .codex/ directory in this PR.