Add support for currentTime, when `status executing`, so it will be visible what is current time of call of `$ --status 8b4d5df0-5a24-4af6-b159-a035463aac68`

[konard]

box@345e83877c14:~$ $ --status 8b4d5df0-5a24-4af6-b159-a035463aac68
4854c1e6-be73-4dd5-8c3a-ff6c8a854993
  uuid 4854c1e6-be73-4dd5-8c3a-ff6c8a854993
  status executing
  command "solve https://github.com/konard/anime-avatar/pull/20 --model opus --interactive-mode --tool claude --attach-logs --verbose --no-tool-check --auto-accept-invite --tokens-budget-stats --auto-attach-solution-summary"
  logPath /tmp/start-command/logs/isolation/screen/4854c1e6-be73-4dd5-8c3a-ff6c8a854993.log
  startTime "2026-04-23T10:02:57.786Z"
  workingDirectory /home/box
  shell /bin/sh
  platform linux
  options
    isolated screen
    isolationMode detached
    sessionName 8b4d5df0-5a24-4af6-b159-a035463aac68
    user false
    keepAlive false
    useCommandStream false
box@345e83877c14:~$ mkdir 1
box@345e83877c14:~$ cd 1
box@345e83877c14:~/1$ $ --status 8b4d5df0-5a24-4af6-b159-a035463aac68
4854c1e6-be73-4dd5-8c3a-ff6c8a854993
  uuid 4854c1e6-be73-4dd5-8c3a-ff6c8a854993
  status executing
  command "solve https://github.com/konard/anime-avatar/pull/20 --model opus --interactive-mode --tool claude --attach-logs --verbose --no-tool-check --auto-accept-invite --tokens-budget-stats --auto-attach-solution-summary"
  logPath /tmp/start-command/logs/isolation/screen/4854c1e6-be73-4dd5-8c3a-ff6c8a854993.log
  startTime "2026-04-23T10:02:57.786Z"
  workingDirectory /home/box
  shell /bin/sh
  platform linux
  options
    isolated screen
    isolationMode detached
    sessionName 8b4d5df0-5a24-4af6-b159-a035463aac68
    user false
    keepAlive false
    useCommandStream false
box@345e83877c14:~/1$ date
Thu Apr 23 10:10:13 UTC 2026
box@345e83877c14:~/1$ 

[konard]

As in #106, we should implement all the same logic in Rust.