Brazilian journalist @rockemgeral just posted a tweet saying "The Cure will play Rio de Janeiro and Sao Paulo in April 2023":
Considering the band just finished their European Tour and will release "Songs of a Lost World" next year, a North and South American tour in 2023 is very likely.
"The Cure are expected to play 50 US shows in sprint/summer 2023 followed up by a Latin American leg of the tour"
https://warp.la/the-cure-estrena-nuevas-canciones-en-sus-shows-en-wembley-225776