Plugins: No progress indicator while site is transferred

[allilevine]

Steps to reproduce the behavior

1. Create a new site with a business plan
2. Go to /plugins or click Plugins in the nav
3. Choose a plugin to install
4. Install the plugin
5. See a progress bar that says "Installling..."

What I expected to happen

More information about what's happening and how long it will take. We've added screens like this to the ecommerce flow: #55073

What actually happened

The progress bar doesn't indicate when the install will be finished, or that other changes are taking place.

Context

This issue was reported in #53911 but I'm adding a separate issue for it.

We'll want to make the same change for sites going Atomic via a theme install.

Does this happen on simple or atomic sites or both?

On Simple sites going Atomic.

Screenshot / Video: If applicable, add screenshots to help explain your problem.