That could be a workaround if I can get it to display the last message first, is there such an option?
Or I can make a keymap that will go directly to the end of the list.

But still it's weird I can't get directly to the popup. If I use the mouse I can click the popup to go to it, but surely that can't be the only way...

You can use <C-w>w to switch to other windows (default Neovim behavior).

OK, so seems that the message is indeed just a window (contrary to what I wrote before) but it seems it is set to be the LAST window in the <C-w>w list, so if you have more than one window, using just <C-w>w you'd have go through all of them.

This can be overcome by using a large counter, e.g. 99<C-w>w will most likely do the trick (can't think of anyone using that much windows...)
Would be a handy keybind to add ("move cursor to last window"), don't you think?

EDIT: I was wrong in my assumption (although it worked at a certain point), the above keybind moves me to the number list...

The correct way to view messages is either by :messages or :Noice history. You can also use :Telescope notify and if you select the message you want it will open in a float window.