feat(core): generalize session input inbox - #36005

Summary

• model user and synthetic messages as variants in one durable Session input lifecycle
• flatten session.prompt() and give session.synthetic() matching delivery, retry, and wake semantics
• migrate inbox rows and durable prompt events to generic session.input.admitted / session.input.promoted events
• promote background completion safely through the inbox and update CLI, TUI, and generated SDK consumers

Validation

• repository pre-push hook: all 31 package typechecks passed
• Core Session and migration tests: 194 passed
• SDK Next tests: 9 passed
• Client tests: 19 passed
• TUI data/row tests: 38 passed
• Legacy package V2 transport tests: 35 passed
• Schema tests: 32 passed

A full Core run also passed 1,249 tests; two unrelated filesystem watcher tests timed out locally.

Design

Implements the design recorded in #35966. Dax's final confirmation remains pending in the linked source thread, so this PR does not characterize the decision as unanimous.

Closes #35924
Refs #35966