Tool list does not refresh on tools/list_changed notification

[xusenlin]

Inspector Version

v0.21.2

Describe the bug

After the server emits notifications/tools/list_changed, the Tools panel
in the UI does not refresh. Manually refreshing is also impossible because
the "List Tools" button becomes disabled once the list has been loaded
(isButtonDisabled={!nextCursor && tools.length > 0} in ToolsTab).
The same issue affects the Resources and Prompts tabs by the same patterns.

Root cause (verified in source)

1. In client/src/App.tsx, the onNotification callback in the
   useConnection hook only handles notifications/tasks/list_changed
   and notifications/tasks/status. There are no handlers for
   tools/, resources/, or prompts/ list_changed, so these
   notifications are received but ignored for refresh purposes.

2. In client/src/components/ToolsTab.tsx (and similarly in
   ResourcesTab.tsx, PromptsTab.tsx), the <ListPane> is rendered
   with isButtonDisabled={!nextCursor && items.length > 0}. Once
   pagination is exhausted, the List button is disabled, so users
   cannot trigger a manual refresh either.

To Reproduce

1. Connect to an MCP server that declares tools.listChanged: true.
2. Click "List Tools" — N tools shown.
3. On the server, dynamically add or remove a tool. Server emits
   notifications/tools/list_changed (visible in Inspector's
   Notifications panel, confirming the wire-level delivery).
4. The Tools panel still shows the stale list.
5. The "List Tools" button is greyed out — manual refresh impossible.
6. The only workaround is to disconnect and reconnect.

Expected behavior

• The Tools panel auto-refreshes (re-issues tools/list) on
  notifications/tools/list_changed.
• The List button stays usable as a manual refresh fallback (perhaps
  showing "Refresh Tools" instead of being disabled when fully loaded).
• Same applies to Resources and Prompts.

Server side

Verified the server is correctly compliant: a raw GET stream shows the
notifications/tools/list_changed event arriving for every server-side
toggle, and a fresh tools/list after the change returns the updated
list. Tested with the official Go SDK
(github.com/modelcontextprotocol/go-sdk v1.4.0) over Streamable HTTP.

Willing to submit a PR

Yes, happy to submit a PR if this is welcome. Could limit it to the
tools tab first, or cover all three (tools / resources / prompts) in
one go — let me know your preference.