feat(mailboxes): postkasser kan forbindes fra fladen

Panelet under Integrationer: tilføj, hent nu, kobl fra. Sit eget frem for en
tilstand mere inde i Gmail-panelet, for de to er ikke det samme i forskellige
klæder — det ene er en app, man logger ind igennem, det andet et kodeord, man
selv holder.

Feltet hedder IMAP-server og ikke Server: der stod i forvejen Server på CalDAV
længere nede, og to felter med samme navn på én side er tvetydige også for en
skærmlæser. Testen fandt det, men det var ikke kun testens problem.

To vagter fangede mangler undervejs, og begge havde ret: mailbox_failed skulle
have en tekst i fladen, ellers ville nogen få serverens engelske logsprog at se,
og de tre ruter skulle i openapi.yaml. Der er nu et Mailbox-skema samme sted, som
siger hvad der ikke kommer tilbage — kodeordet og eventuelle tokens.

E2E-prøven forbinder til noget, der ikke lytter, og ser efter værtens egen
afvisning på skærmen. Den er samtidig prøven på at 422 var det rigtige valg: var
det stadig 502, ville et mellemled kunne kaste beskeden væk, og der ville stå
"noget gik galt".

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

docs/openapi.yaml

@@ -2477,6 +2477,86 @@ paths:
                   created: { type: integer }
         "502": { $ref: "#/components/responses/Upstream" }
 
+  /api/v1/mailboxes:
+    get:
+      tags: [integrations]
+      summary: The mailboxes this person has connected.
+      responses:
+        "200":
+          description: OK
+          content:
+            application/json:
+              schema:
+                type: object
+                properties:
+                  mailboxes:
+                    type: array
+                    items: { $ref: "#/components/schemas/Mailbox" }
+    post:
+      tags: [integrations]
+      summary: Connect a mailbox over IMAP.
+      description: >
+        The connection is tested before it is saved, so a mailbox that cannot be
+        read is refused here rather than failing quietly every ten minutes.
+      requestBody:
+        required: true
+        content:
+          application/json:
+            schema:
+              type: object
+              required: [host, username, password]
+              properties:
+                name: { type: string }
+                host: { type: string, example: "imap.mail.me.com:993" }
+                username: { type: string }
+                password: { type: string, description: "An app-specific password on every host worth naming. Stored sealed." }
+                folder: { type: string, default: INBOX }
+      responses:
+        "201":
+          description: Connected
+          content:
+            application/json:
+              schema: { $ref: "#/components/schemas/Mailbox" }
+        "400": { $ref: "#/components/responses/BadRequest" }
+        "409": { description: That mailbox is already connected }
+        "422": { $ref: "#/components/responses/Upstream" }
+
+  /api/v1/mailboxes/{mailboxID}:
+    delete:
+      tags: [integrations]
+      summary: Disconnect a mailbox. The tasks it made stay.
+      parameters:
+        - name: mailboxID
+          in: path
+          required: true
+          schema: { type: string }
+      responses:
+        "204": { description: Disconnected }
+
+  /api/v1/mailboxes/{mailboxID}/sync:
+    post:
+      tags: [integrations]
+      summary: Read one mailbox now.
+      parameters:
+        - name: mailboxID
+          in: path
+          required: true
+          schema: { type: string }
+      responses:
+        "200":
+          description: OK
+          content:
+            application/json:
+              schema:
+                type: object
+                properties:
+                  created: { type: integer }
+                  partial:
+                    type: boolean
+                    description: The run hit its time budget. What it made is kept.
+        "404": { $ref: "#/components/responses/NotFound" }
+        "422": { $ref: "#/components/responses/Upstream" }
+
   /api/v1/ai/settings:
     get:
       tags: [integrations]
@@ -3082,6 +3162,20 @@ components:
                 items: { type: string }
 
   schemas:
+    Mailbox:
+      type: object
+      description: One connected mailbox. The password and any token are never returned.
+      properties:
+        id: { type: string }
+        kind: { type: string, enum: [gmail, imap] }
+        name: { type: string }
+        host: { type: string }
+        username: { type: string }
+        folder: { type: string }
+        last_uid: { type: integer }
+        last_sync_at: { type: string, format: date-time }
+        created_at: { type: string, format: date-time }
+
     Error:
       type: object
       description: |