fix(desktop): a sign-in stays visible when the same profile is picked again

Review round 3: on a multi-connection desktop the scope selector pins
`{connectionId, profile}` while an operation started from the ambient
scope holds the bare profile name, so re-picking the same profile hid
the open sign-in. Scopes now compare by the backend they resolve to
(connection, else the active one, plus profile).

apps/desktop/src/app/capabilities/connectors/data/account-operations.test.ts

@@ -24,4 +24,10 @@ describe('accountOperationFor', () => {
     expect(accountOperationFor(operations, 'gmail', { connectionId: 'remote', profile: 'home' })?.opId).toBe('b')
     expect(accountOperationFor(operations, 'gmail', 'other')).toBeNull()
   })
+
+  it('treats a bare profile and the same profile pinned to the active connection as one scope', () => {
+    const operations = { a: operation('a', 'home') }
+
+    expect(accountOperationFor(operations, 'gmail', { connectionId: 'local', profile: 'home' })?.opId).toBe('a')
+  })
 })

apps/desktop/src/app/capabilities/connectors/data/account-operations.ts

@@ -6,8 +6,10 @@ import type {
 } from '@hermes/shared'
 import { atom } from 'nanostores'
 
-import { type ProfileScope, profileScopeKey } from '@/hermes'
+import type { ProfileScope } from '@/hermes'
 import { type ConnectionTarget, parseConnectionTarget } from '@/store/connection-request'
+import { activeGatewayConnectionId } from '@/store/gateway'
+import { normalizeProfileKey } from '@/store/profile'
 
 import { invalidateConnectors } from './keys'
 import { accountOperationStatus } from './rpc'
@@ -44,16 +46,28 @@ function resumeConnect(slugs: readonly string[]): void {
 const parseTargets = (targets: ConnectionUpdatePayload['targets']): ConnectionTarget[] =>
   targets.map(parseConnectionTarget).filter((target): target is ConnectionTarget => target !== null)
 
+// A bare profile name rides the active connection, so `'home'` and `{connectionId: <active>, profile: 'home'}` are
+// the same backend and must match.
+function resolvedScopeKey(scope: ProfileScope): string {
+  const active = activeGatewayConnectionId() ?? 'local'
+
+  if (scope instanceof Object) {
+    return `${(scope.connectionId ?? '').trim() || 'local'}::${normalizeProfileKey(scope.profile)}`
+  }
+
+  return `${active}::${normalizeProfileKey(scope)}`
+}
+
 /** The open (else newest) operation for one app in one profile scope; other profiles' sign-ins are not this one's. */
 export function accountOperationFor(
   operations: Readonly<Record<string, AccountOperation>>,
   slug: string,
   scope: ProfileScope
 ): AccountOperation | null {
-  const key = profileScopeKey(scope)
+  const key = resolvedScopeKey(scope)
 
   const mine = Object.values(operations).filter(
-    operation => operation.connectors.includes(slug) && profileScopeKey(operation.scope) === key
+    operation => operation.connectors.includes(slug) && resolvedScopeKey(operation.scope) === key
   )
 
   return mine.find(operation => !operation.settled) ?? mine[mine.length - 1] ?? null