What are good high level non-combat encounters?

Disaster relief. If your players are good-inclined, they have a wide variety of abilities that would be helpful in saving a community from fires, plagues, earthquakes and more.

Otherwise, something like an encounter with the wild hunt or another plane's equivalent. They don't start hostile and have confusing rules the party need to Intuit to avoid negative consequences or violence

High tier is not so much about how hard something is to do, and more about the choices they have to make. For example, my L18 party is about to have choose between cutting the legs out from under the upcoming ilithid invasion, thereby saving millions of lives, or saving the paladin's beloved homeland.

• Contested succession or political election situation. Give the candidates qualities that appeal to and are disliked by different party members. Expect them to put themselves forward as 3rd party candidates so have a plan for that.
• Hostage situation
• Curse then with something that needs wish to solve. I'm running The Scriveners Tale from Candlekeep Mysteries right now and it's the most heartburn my level 14 party has had in a long time.
• World ending shit where they can't (or probably can't) stop everything bad from happening. Make them choose to save the city or their favored NPC.

They've basically turned into superman by the time they're 3rd or 4th tier so hit them with the line of stuff that makes for interesting superman stories.

Good ol' fashion Wizard Maze! Magical solutions are impossible due to magic cancelling effects within the maze itself.

Noncombat encounters are pretty similar across levels, just with higher stakes. Instead of negotiating with city officials, the negotiate with kings and emperors.