If the chainrings are worn into a shark tooth profile a new chain is likely to slip under load. I wouldn’t be able to tell where the chain is slipping just that the cranks suddenly slip round under load. If you use one chaing ring less than the others test in the least worn (big ring if you have triple is unlikely to get as much use off road). If that improves things then chain ring wear is likely.
If it is worn chainrings then put your old chain and cassette back on if you still have them and run into the ground before replacing.