System Information
Operating system: Windows 10
Graphics card: Any

Blender Version
Broken: 2.80

Description of error
If you select a tool in any editor that is not the 3D Viewport, then the tool is not updated in the properties editor's tool tab.

Exact steps for others to reproduce the error

• Go in the UV editing workspace,
• Select the tool tab in the editor properties,
• Select a tool in 3D Viewport (the tool is updated in the editor properties),
• Select a tool in the UV editor (the tool won't be updated in the editor properties).

Suggested Solution

The tool tab is currently tracking the last tool used in 3D Viewport.

Solution 1 is to make the tool tab track the last tool used in any editors.

Solution 2 is to add a dropdown list in the tool tab so that the user can chose whether to track: last used tool, 3D viewport, UV editor, Image Editor, Shader Editor, etc...
Note that Solution 2 makes the tool tab more flexible for multi-monitors situation.

Related Link
I reported it as a papercut here: https://devtalk.blender.org/t/blender-ui-paper-cuts/2596/3402?u=nodragem
Then it was highlighted as a bug here: https://devtalk.blender.org/t/blender-2-8-user-interface-design/505/1448?u=nodragem