OutboxRouter does not forward `routers` to the inner broker

[lesnik512]

What

OutboxRouter.__init__ (faststream_outbox/fastapi/router.py) mirrors most of
OutboxBroker.__init__'s kwargs and forwards them through StreamRouter's
**connection_kwars, but routers is not among them. OutboxBroker(..., routers=[...]) works;
OutboxRouter(..., routers=[...]) is a TypeError.

dlq_table and metrics_recorder were the other two gaps here and were forwarded in #88, which
left routers as the only unforwarded OutboxBroker argument.

Why it is still open

Unlike dlq_table / metrics_recorder, this is not mechanical. OutboxRouter is itself a
StreamRouter, so app.include_router(router) already contributes the router's own subscribers via
the FastAPI lifespan. A separate routers sequence would introduce a second, differently-timed
source of subscribers into the same broker, and its behaviour is unsettled on two axes:

• Start / lifespan — when do the nested routers' subscribers start relative to the FastAPI
  lifespan, and what happens if the app never includes the outer router?
• AsyncAPI — how the nested routers' channels and operations compose into the document the
  router serves at schema_url (default /asyncapi).

Forwarding the kwarg without settling those would ship whichever behaviour falls out of
StreamRouter's ordering, which is not obviously the one a user would expect.

Workaround

Register subscribers directly on the OutboxRouter — @router.subscriber(\"queue\") — rather than
composing sub-routers under it. Nothing is unreachable today.

Revisit trigger

A concrete "include a sub-router under the FastAPI outbox router" demand from someone hitting it,
rather than a hypothesised one. That report is also what would pin down the expected lifespan and
AsyncAPI semantics, which is the part currently missing.

Context

Carried over from planning/deferred.md, retired when the repo adopted the PR-body-as-spec
convention. Originally surfaced as F8-01 in the 2026-06-14 pass-3 audit, which confirmed the
dlq_table / metrics_recorder half was mechanically forwardable and flagged routers as the part
warranting a design call.