You can continue at the start of your current round. You have 3 lives, after that you need to restart at round 1. But you are not alone in missing that, the UI is not very intuitive. There are 2 buttons when you die, the top one lets you continue at your current round, the second one restarts the game.
I do have some plans vampire survivors like upgrades between rounds. But it will be nowhere near Vampire Survivors craziness as I still want the players skill to be the focus.