Report more statuses of remote actions in the UI

### Description of the feature request:

When Bazel is running remote actions, it is unclear what the remote path is doing. The UI already reports "scheduling" and "downloading outputs" separately, but there are other cases that would be great to surface in the UI:

* **Uploading inputs.** This information is available in the JSON profile so I suppose it would be pretty easy to surface in the UI.

* **Staging inputs on the remote worker / saving outputs to the remote cache.** I have no idea if this is visible from Bazel's perspective. I doubt it, but mentioning it anyway. If the information is available, it'd be awesome to also surface this to assist in debugging slow remote execution issues.

### What underlying problem are you trying to solve with this feature?

Better understand the behavior of Bazel when the remote build farm or the remote cache are slow.

### Which operating system are you running Bazel on?

N/A

### What is the output of `bazel info release`?

bazel-6.1.1

### If `bazel info release` returns `development version` or `(@non-git)`, tell us how you built Bazel.

_No response_

### What's the output of `git remote get-url origin; git rev-parse master; git rev-parse HEAD` ?

_No response_

### Have you found anything relevant by searching the web?

_No response_

### Any other information, logs, or outputs that you want to share?

_No response_

Start by tracing the UI reporting for the existing “scheduling” and “downloading outputs” statuses, then inspect the JSON profile where uploading-inputs information is available. Determine which remote-action stages Bazel exposes, and consider the work complete when the available statuses are surfaced clearly in the UI.

Written by the indexing model from the issue text.