Hide agent host tip if user manual selects via picker

[anthonykim1]

Resolves: #322453

• Make chat input notifications evaluate session-type filters against the pending delegation target before the backing session resource.
• Rerender input notifications when the user changes the pending delegation target from the session picker.
• Preserve model-pool validation semantics by leaving getCurrentSessionType() based on the real session resource.
• Add a browser regression test covering local-only notification visibility when switching to and from Agent Host.

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Inspirations from:

• The distinction between real session resource and picker/delegate state comes from ChatInputPart.getCurrentSessionType.
• The explicit rerender hook for session-type-gated notifications comes from ChatInputNotificationWidget.rerender.
• The local-only tip behavior comes from LocalAgentDisabledInputTipContribution.

[Copilot]

Pull request overview

This PR fixes chat input notification visibility when the user switches the session target via the session picker (e.g. “Continue in Agent Host”), by evaluating session-type-gated notifications against the pending delegation target and forcing a rerender when that pending target changes.

Changes:

• Added getNotificationSessionType() so input notification filtering prefers _pendingDelegationTarget (then _currentSessionType, then the real session resource type).
• Triggered ChatInputNotificationWidget.rerender() when the pending delegation target changes via the picker, ensuring session-type-gated tips hide/show immediately.
• Added a browser regression test to verify rerendering updates session-type filtering behavior.

Show a summary per file

File	Description
src/vs/workbench/contrib/chat/browser/widget/input/chatInputPart.ts	Uses a notification-specific “effective session type” and rerenders notifications when the pending delegation target changes.
src/vs/workbench/contrib/chat/test/browser/widget/input/chatInputNotificationWidget.test.ts	Adds a regression test for session-type-gated notification visibility when the session type provider changes and rerender() is invoked.

Copilot's findings

• Files reviewed: 2/2 changed files
• Comments generated: 2