The short answer
No. Demo progress does not continue into the full game. Your Demo save can instead qualify you for Kubi Akari, an equippable charm.
How to claim Kubi Akari
Capcom’s official Demo page gives the following claim sequence:
- Keep your Demo save data.
- Open Settings → Privacy → Demo Bonus → Collect Reward.
- Once a Spirit Mirror is available, open its add-on content menu, then choose Demo Bonus to claim the charm. Capcom lists several English labels for that menu: Additional Content, Add-on Content, Add-ons or Downloadable Content.
- Once charm equipment is unlocked, open Main Menu → Equipment → Charms to equip Kubi Akari.
Capcom says Spirit Mirrors and charm equipment unlock separately. If you can claim the item but cannot equip it yet, the equipment feature may still be locked.
These are official published instructions, not a hands-on walkthrough. Capcom does not specify an exact unlock chapter or numerical charm effect on that page.
What does not transfer?
Demo story progress and your position in its route do not carry over. Capcom’s Steam announcement distinguishes the save-data reward from continuing a Demo save.
If the reward does not appear
Keep the save intact and check the game’s current support information. The cited instructions do not establish cross-platform eligibility, account-matching rules, or a recovery procedure. Do not delete or replace saves to try to force the reward.
For the separate purchase-period items, see editions and Early Adopter bonuses.