Can I add Browser (Edge or Chrome) websites to the shelves/docks? I currently use Speedial but it seems to be compromising/intercepting my URLs. I don't trust it anymore, but I do love how it looks.

Easiest way is to just drag & drop the URL from the browser's address bar into the dock.

Alternatively you can manually add items (Insert New Item -> Item), select 'URL' type in the dialog box that pops up and type in the URL of the site.

Thanks for the fast response!

Pasting the URL worked. As far as seeing a new item pop-up for URL, I don't see that. Here is a screenshot:

You select "Item" at the top of the insert context menu, which opens the Item Properties dialog. Then on that dialog you change the 'Item type" to URL, then type in the label and the actual URL and press OK.