Split the pipeline by dialect over the shared loop

[peteski22]

Problem

_pipeline.py is 4,672 lines, imported by about 30 modules pulling about 80 names. Its interface is wide, so it is a collection of loosely related helpers rather than a module with a small interface.

Proposal

One shared loop and three dialect adapters (chat, messages, responses); the rest of _pipeline.py moves to the domain it serves. Public surface shrinks to a handful of entry points.

Acceptance

• Importing modules count and imported names recorded before and after.
• Target under ten names.
• The integration suite passes.

Depends on

#1198, #1194.

Part of #1171.

[peteski22]

#1366 grew api/routes/_pipeline.py from 4,969 to 5,261 lines (d311450c to 9c8acdec). It is 5,261 lines at f82dbc33. Tracked in #1470.