Remove unneeded sidebarAction in main.background

[djsmith85]

Type of change

- [ ] Bug fix
- [ ] New feature development
- [X] Tech debt (refactoring, code cleanup, dependency upgrades, etc)
- [ ] Build/deploy pipeline (DevOps)
- [ ] Other

Objective

Remove unneeded sidebarAction in main.background

With #3571 the updating of the badge got refactored. Moving this variable/action into browserApi.getSidebarAction

Code changes

• apps/browser/src/background/main.background.ts: Removed declaration and defintion of sidebarAction

Before you submit

• Please add unit tests where it makes sense to do so (encouraged but not required)
• If this change requires a documentation update - notify the documentation team
• If this change has particular deployment requirements - notify the DevOps team