Need different activity indicators for sessions

### Feature summary

Different session activity indicators will help me figure out what stage a session is at

### What problem are you trying to solve?

Right now, any time the agent is active for a session, the state in the nav pane shows the blue dots.

However, this makes it hard to distinguish between two unique states that have different implications for me the developer.

Once I start a session for an issue, it begins with `analyzing the issue` and potentially asking me some questions before giving me the option to let it build the solution on autopilot. It's important to distinguish this state from the `building on autopilot` state.

In the first case, `analyzing the issue`, I can expect to be engaged fairly soon as the agent asks clarifying questions and requests approval to start building. When it's done with this stage it will stop and wait for me - I generally want to wait until I've approved building before I get to distracted with other work.

In the second case, `building on autopilot` , I expect the agent to keep building until the code is done, tests are run and the PR is merged. This will typically take much longer and when it's done it's in theory done-done (though see my other issue on Agent Merge frustration). This is ideal the agent shouldn't need my help with anything and I can work on other things, eat lunch, go to bed, or whatever floats my boat.

What I need is a visual indicator on the session to know which state it's in so I can quickly tell if a session is likely to need help from me soon.

### Proposed solution

_No response_

### Workflow impact

_No response_

### Installation context

_No response_

### Additional context

_No response_

Start by tracing how session activity is represented and rendered in the navigation pane. Identify the states for analyzing the issue and building on autopilot, then determine how each should be visually distinguished. Done means users can tell these states apart at a glance, with coverage for the relevant session-state behavior.

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