There is auto-save when playing on itch.io through a web browser.
Are you asking about cross-platform saves? Right now, save data is stored locally on your device. That means if you switch devices, you’ll need to start over.
You might be able to transfer your save manually by extracting it from your browser’s local storage and moving it to another device, but I haven’t tested this myself. So please be careful, as it could potentially corrupt your save.