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When saying pinned tabs, you mean shortcuts, right?

I have added these suggestions to the to-do list and should come out in the next update!

Yes, I did not know what they were called.

Currently, you can't. Chrome doesn't have a built-in API for getting these, but you can have a bookmarks widget.

What about Firefox? Which is what I am using.

After some research, it doesn't seem like Firefox supports it.