[Dev UI] Refactor / consolidate Trace Drawer into a common place

[MichaelDoyle]

We're over due for consolidating the Trace Drawer code into a common place.

1. It would be really cool to have something similar to:

   export abstract class TracerDrawerComponent {
     // trace drawer specific code
   }
   
   export class PromptRunnerComponent extends TracerDrawerComponent {
     // etc, etc
   }

   Gemini also suggested a Typescript mixin, which could also work. I hadn't considered it before.

2. We also have to deal w/ the html templates. Right now, every component that needs to show the trace has to wrap its entire html template in a <mat-drawer-container.

   One idea is that the "home" component should actually have the drawer, since it's already got the <router-outlet> that renders all the pages inside, and wire that up. More and more this is starting to feel like a top level app concern.

cc @tonybaroneee @shrutip90 @mjchristy