fix(omp): resume by mode, not silently as claude, and support --continue

resumeHistorySession() never sent mode when recreating a session from a
history/session-manager row, so the server default silently opened a
plain Claude session for every non-claude row -- reproduced live: OMP
rows spawned Claude sessions on click. Thread the row's mode through
every call site (welcome list, session manager, mobile overview) and
only send the Claude-specific resumeSessionId for claude rows.

Codeman has no live PTY-reattach outside server boot, and it's moot for
OMP anyway (exiting it kills the pane's only process), so route the
non-claude relaunch through each CLI's own continue-most-recent flag
instead of a context-free fresh start. OMP never got one: buildOmpCommand
only implemented --model/--resume despite omp --help documenting
-c/--continue. Added continueSession to OmpConfig end-to-end (type,
schema, builder) mirroring the existing opencode/pi/grok/deepseek
fields, and wired resumeHistorySession to use it.

Verified live: told a real omp session a secret, exited it, closed the
tab without killing tmux, relaunched with --continue in the same
directory, and had it recall the secret.

test/command-palette-ui.test.ts

@@ -401,7 +401,7 @@ describe('Session Manager unified list', () => {
     const [historyRecord, , historyOptions] = app._buildHistoryItem.mock.calls[1];
     expect(historyRecord).toMatchObject({ sessionId: 'conv-uuid-1', sizeBytes: 2048, firstPrompt: 'old prompt' });
     historyOptions.onActivate();
-    expect(app.resumeHistorySession).toHaveBeenCalledWith('conv-uuid-1', '/repo/old');
+    expect(app.resumeHistorySession).toHaveBeenCalledWith('conv-uuid-1', '/repo/old', undefined, undefined);
   });
 
   it('surfaces an error message instead of an empty list when the endpoint fails', async () => {

test/omp-mode.test.ts

@@ -85,6 +85,26 @@ describe('OMP spawn command', () => {
     ).toBe('omp');
   });
 
+  it('continues the most recent session when no explicit resume id is given', () => {
+    expect(
+      buildSpawnCommand({
+        mode: 'omp',
+        sessionId: 'abc12345',
+        ompConfig: { continueSession: true },
+      })
+    ).toBe('omp --continue');
+  });
+
+  it('prefers an explicit --resume id over --continue', () => {
+    expect(
+      buildSpawnCommand({
+        mode: 'omp',
+        sessionId: 'abc12345',
+        ompConfig: { resumeSessionId: 'session-99', continueSession: true },
+      })
+    ).toBe('omp --resume session-99');
+  });
+
   it('drops unsafe model strings from the spawn command', () => {
     expect(
       buildSpawnCommand({