Click and hover events still work when F1 is toggled

The bug

Click and hover events still work for chat messages even if the chat is hidden using F1.

How to reproduce

1. Run this command:

   /tellraw @s {"text":"Hover over me after pressing F1","hoverEvent":{"action":"show_text","value":"You should not see this; also click me"},"clickEvent":{"action":"run_command","value":"/say Clicked"}}
   

2. Toggle F1
3. Open chat (Press T)
4. Point your mouse to the text
   → The hover text still appears, clicking at its position also runs the clickEvent