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.

src/web/public/session-ui.js

@@ -692,7 +692,7 @@ Object.assign(CodemanApp.prototype, {
         btn.append(...parts);
         btn.addEventListener('click', (e) => {
           e.stopPropagation();
-          this.resumeHistorySession(s.sessionId, s.workingDir, s.name);
+          this.resumeHistorySession(s.sessionId, s.workingDir, s.name, s.mode);
         });
         container.appendChild(btn);
       }