The new quest log will not admit I have a new mission, let alone let me complete it. When I try switching to the old quest log I can't even see a single quest (completed or not). The quests that I have completed and that did show up are not disappearing either, and keep trying to make me claim my reward (but I can't)
I've tried refreshing the page and logging out and back in.

Sorry if this isn't very clear I can always try to explain some more/ fiddle with photos

What quest are you specifically having issues with?

Missions are separate and are what you send pets on. They can be accessed under Explore -> Mission Log.

Specifically quest from the quest boards. I picked up a new quest yesterday (when I sent ticket) and went ahead and completed it. I went to go "finish" the quest (complete the quest?) and grab rewards. There was no new quest listed on my log to complete, even though the tab "explore" and "quest log" was orange.

Another side note (idk if this is normal or not) but I finished a quest and claimed my reward, but the quest log still shows the quest as "completed" and still is trying to make me claim an item. I can't actually click anything

Edit: After checking today everything seems normal now. I'm suspecting it may be the browser I use (Firefox). Sorry for the bother haha I think I need to switch to Chrome