tim plugin, chat bot sync notifications, test fixes

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

public/plugins/tim/README.md

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+# tim plugin
+
+Tiny time calculator. Three tabs: duration between two times, add a duration to a time, and workday-end with a break.
+
+## Open
+
+- **`I`** on the board
+- **Clock icon** in the card-edit toolbar
+- Terminal: `tim`
+
+Close with **ESC** or the × button.
+
+## Tabs
+
+### Duration
+Two HHMM inputs → how many hours and minutes between them. Wraps past midnight.
+
+### Add
+Time + duration → resulting HHMM. Wraps around 24h.
+
+### Workday
+Start, break from, break back, target (defaults to 08:00). Computes when the workday ends to hit the target, or tells you it's already reached.
+
+## Input format
+
+All inputs take HHMM-style strings:
+
+- `0830`, `830`, `08:30`, `8:30` → 08:30
+- Missing digits are left-padded with zeros
+- Minute component must be < 60
+
+Invalid input clears the result silently — no red flashes while typing.
+
+Calculation is live: the result updates as you type in each field.
+
+## Disabling
+
+Add `"tim"` to the `disabled` array in `data/plugins.json`.