I just purchased Affinity Designer and these are my first few hours of use on a Mac. I have tried to get the Character and Paragraph panels to show up the many ways that have been shared by others. However, nothing ever shows up. I even turned off all the other panels in View > Studio so I could be sure they weren't just hidden from view. Nothing.
I found a screenshot of someone else's (https://forum.affinity.serif.com/index.php?/topic/25173-things-i-cant-do-in-affinity-designer/?hl=paragraph+panel&p=119628) so I know I'm looking in the right place and it never shows up.
Anyway, I thought you might ask if any other panels weren't working so I went through each and every one of them and they all worked. Still no Character or Paragraph... but I noticed the 'Reset Studio' option in View > Studio and wondered what it was. So I clicked it. Then I tried clicking the Character and Paragraph buttons in the main toolbar again and voila! Now they appear. Thought you'd want to know in case it happens to someone else.