Agent Picker is not pre-selected when creating a new Agent Host session with specific Agent in Agent Window

[DonJayamanne]

Blocked on #317848

Steps to repro

• Start a new Chat Session in Agents Window
• Select vscode fodler
• Select Copilot CLI Local Agent Host
• Select a custom agent from the agent picker
• Enter the prompt what is the time
• Hit the send button
• Then wait for new session to start
• You'll see that the new chat session doesn't have the agent selected in the Agent Picker

[DonJayamanne]

Lets assume we pick the custom agent Data from the agent picker

Note: All of the following steps run synchronously

Problem

• ChatInputPart.setInputModel is invoked with the model IInputModel
  This has the correct agent, model information,
• The line const chatModes = this.chatModeService.createModes(forSessionResource); runs next
  Here we build the ChatModes service & this will fetch the list of custom agents in the background in ChatModes class ctor this._pendingRefresh = this.refreshCustomPromptModes(true);

Note: The list of agents is now being fetched asynchronously in the background.
I.e. its async

• The line this._modelSyncDisposables.add(autorun(reader => { runs next
• Next ChatInputPart._syncFromModel is executed
• Next ChatInputPart.setChatMode is executed
• Now, we have const mode2 = modes.findModeById(mode) running
  However the list of agents is still being fetched asynchronously in background
  So, now the agent Data cannot be found in the list of know agents, as a result the agent picker reverts to the default agent!

Not sure ChatModes is the right way, perhaps we do need the more generic ChatModeService
Not sure.