Simplify badge icon logic

[jonathansampson]

Removes redundant lookups, invalid considerations, and handles older patterns.

• Submitted a ticket for my issue if one did not already exist.
• Used Github auto-closing keywords in the commit message.
• Added/updated tests for this change (for new code or code which already has tests).
• Ran git rebase -i to squash commits (if needed).

Fixes #6193

Test Plan:

An extension's manifest file may contain a browser_action.default_icon property. This property usually holds an object, but may (in older extensions) hold a string. String paths to images were not being handled by Brave, which caused some extensions (such as Vimium) to have no displayed icon.

To test this, install the Vimium extension in your development build of Brave. Vimium's extension ID is dbepggeogbaibhgnhhndojpepiihcmeb. With this extension registered and loaded, running Brave should reveal the Vimium icon near the Brave Shield icon.

This commit also prevents the redundant look-up of manifest.browser_action.default_icon (path is already a reference to browser_action.default_icon). Also, manifest.icons should not be the source for browser action icons.

[jonathansampson]

bump for review @darkdh @bridiver

[bridiver]

lgtm

[darkdh]

++