Improve live timer sync on home and timers pages

[Fingolfin7]

Motivation

• Timers started/stopped outside the web UI (e.g. via the CLI/API) were not reflected promptly on the timers page or the home timers section, requiring manual refreshes.
• The previous JS updated every .card on the page which touched unrelated elements and performed unnecessary DOM work.

Description

• Limit duration updates to timer cards inside #active-timers by changing the selector to #active-timers .card[id^="timer-"] in core/static/core/js/dynamic_timers.js to avoid touching unrelated cards.
• Add a polling sync loop in core/static/core/js/dynamic_timers.js that calls /api/list_active_sessions/ every 5 seconds and compares server-side active session IDs with locally rendered timer IDs, triggering window.location.reload() when they differ so CLI/API changes appear quickly.
• Add helper getLocalTimerIds() and syncActiveTimers() in the same JS file to support the above comparison and run an initial sync on page load.
• Update list_active_sessions in core/api.py to apply filter_by_active_context(...) so the polled API mirrors the UI's active-context filtering and avoids false positives when comparing IDs.

Testing

• Ran python manage.py check which failed in this environment because required environment variables are not set (SECRET_KEY), so the project-level Django system checks could not complete; no other automated tests were executed in this session.

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Codex Task