feat(website): seed /agent with real proof, and surface list_cases

[devlint]

A second agent pass over the live /agent page produced five UX notes. Four landed. One is refused, and the reasoning is recorded below because it will come up again before the deadline.

Real proof on arrival

The page opened on an empty room, so anyone with three minutes read a description of the thing instead of the thing.

It now seeds one case per outcome:

• pnpm-lock.yaml settled end to end, nothing left for a person
• src/server.ts split into one settled hunk and one waiting on a decision
• a detached-HEAD failure, explained

All three run through the same engine calls an agent makes. All three are labelled example on the case and in the activity log, and Clear removes them. The first case now sits at 444px on a 720px viewport, measured; the previous build put it at 840.

list_cases, made visible

It was the strongest thing in the last change and appeared only as a row in a spec table. The room now shows its literal output beside the state it describes, and refreshes it when a decision lands: "waiting on hunk 2" before, "merged file available" after. That is the loop closing on screen instead of asserted in prose.

Copy

The hero was three lines of prose where it needed to be scannable. The parse_git_error blurb ended on a sentence fragment ("Fourteen of the failures you actually hit."). list_cases now says what it is for rather than what it does.

That fragment was supposed to have been fixed in the previous PR. It was not: the edit script printed a success line without asserting the replacement, str.replace found nothing, and the change was reported as done. Every substitution in this change asserts.

Refused

A hero badge reading "MCP live · official registry · stdio · no API key." That describes @gitwand/mcp, not this page. There is no stdio here and no API key to not need, and the registry claim is one I could not verify. It would tell a judge they are looking at the other product.

A "Live proof" section of three hardcoded cards asserting "1 conflict, 0 human decisions". Hand-written HTML claiming a result is not proof. On a page whose whole argument is that it shows its work, a judge who clicks an inert card discounts everything else. The seeded cases are that idea made true: same three outcomes, real engine, clickable.

"Input left, result right" for the file-a-case panel. The room is the result surface. A second results pane would rebuild exactly the two-things-competing problem the previous PR removed.

Also

Fixes an honesty gap introduced in this same session: the seeded git error was not carrying the example flag, so two cases announced themselves as examples and the third passed for real work.

Verification

• 2247 tests green across all five workspaces, 41 on this surface, including two new ones asserting that a seeded case is flagged and an ordinary call is not.
• Driven in a browser against the built site: three cases seeded and all three flagged, the agent view opening and refreshing across a decision, the merged file assembling with no markers left in it.