Once The Bathhouse Restored Edition officially releases on Steam, if you own the old TBH in your Steam library, you will receive the game in your Steam library for free!
If you own the old TBH, you'll get TBHRE in your library for free!
Source: Steam Community (opens in a new tab)
Build and release context
Recorded Steam release date:
Within one calendar day of this post (UTC). The listed date does not establish an exact launch time.