I agree. The tooltips in general is not a great user experience. I considered implementing something better for some time now: #83 #84 #85

if a click on the area where the tooltip is activate would fix the toop, with a click outside of the tooltip (and maybe an x at the top right) deactivating the fixation

This will probably mess up all the touch screens. Might work given some effort though. But technically it would be just easier to have a normally positioned, conventional popup window, like the one with changelog, or similar to what auspice tree has. Could also fit a lot more data and be scrollable.

What about adding a delay on purpose during which time one can move the mouse over the tooltip to fix it in place until the mouse moves away? This would not degrade touch experience

Just as a workaround, I found (at least on Windows 10 chrome) if you get the pop-up up, right-click the mutation, then move your mouse over the pop-up, left-click to dismiss the 'right-click-menu' then you can move the mouse around within the popup, copy text, etc.
Here's a gif:

(Sorry I don't know why the colours are weird - that's definitely from making the gif, not how the Nextclade page is actually showing up for me.)

I made a little prototype #749