[FEATURE] Allow browser widgets inplace of the Dock Search Bar

[pranavsetpal]

Describe the feature

Allow the user to select a browser(or anything for that matter) widget which fits the Dock dimensions.

Why would it be useful to add?

In my particular case, I use searx as my search engine. Due to the nature of searx really, Lawnchair would be only able to support at most one instance of it. I can use my browser(Firefox) to use whichever instance I like. Being able to replace the dock with the browser's search widget would alleviate the issue of my preferred search engine not being present.

This of course solves the issue for anyone else whose search engine is currently not supported.
In my opinion, it also makes sense to let the browser handle which search provider to use, and let Lawnchair make sure you can access that as easily as possible. Lawnchair currently also simply opens the search engine's website in the browser and nothing more, so the experience wouldn't change for the worse for anyone. P.S. In case one uses the app option for a search provider, that will be supported by this feature as well, as the app would have a search widget which the user can simply place in the Dock.

Did the feature exist in Lawnchair v2? (Play Store version)

No

Example(s)

Additional context

No response