fix(docker): carry the owned flag on the wire the way master already does

The cherry-picked "copy an existing case" commit declared a second
`CaseInfo.docker.owned` and emitted `owned: true|false` on every docker
case, while master had meanwhile shipped the same field from the
adopted-container work with a narrower wire shape: `owned` is present
only when false, absent means owned. Two declarations failed typecheck,
and two emit styles on one response would have made the picker's answer
depend on which read path filled it.

Keep master's shape at both response sites (the case list and the
single-case lookup, which lacked the field entirely), fold the picker's
reason for the field into the existing doc comment, and repoint the test
that pinned "set on exactly two sites" at the surviving form, adding a
negative pin so the duplicate style cannot come back.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

test/docker-adopt-duplicate.test.ts

@@ -27,13 +27,16 @@ describe('the API exposes what the picker needs', () => {
   it('reports whether the container is owned, on EVERY case-shaped response', () => {
     // Two sites build a docker CaseInfo (the list and the single-case lookup);
     // filling only one leaves the picker blind depending on which the UI read.
-    expect(routes.match(/owned: dockerCase\.owned !== false,/g) ?? []).toHaveLength(2);
+    expect(routes.match(/\.\.\.\(dockerCase\.owned === false \? \{ owned: false \} : \{\}\),/g) ?? []).toHaveLength(2);
   });
 
   it('treats an ABSENT owned flag as owned, so legacy cases are not offered', () => {
-    // `owned` is optional and predates this field; truthiness would read a legacy
-    // case as adopted and offer a duplicate the server then refuses.
-    expect(routes).toContain('dockerCase.owned !== false');
+    // `owned` is optional and predates this field; the wire carries it ONLY when
+    // false (absent = owned, the shape master already used), so the picker must
+    // test `=== false` rather than truthiness, or a legacy case would read as
+    // adopted and be offered a duplicate the server then refuses.
+    expect(routes).toContain('...(dockerCase.owned === false ? { owned: false } : {}),');
+    expect(routes).not.toContain('owned: dockerCase.owned !== false');
   });
 });