Atlus has not yet officially announced the western release date for Shin Megami Tensei III: Nocturne HD Remaster, but Nintendo suggests that it be released in May.
In the most recent press release referring to the new features of the Nintendo eShop, Nintendo informs that Shin Megami Tensei III: Nocturne HD Remaster has become available for pre-order and that it will cease to be from 25 May 2021, suggesting that this is the date of launch for the remaster.
As mentioned, Atlus has not yet officially confirmed, but Nintendo seems to have moved ahead.
Another recently discovered information, thanks to Gematsu, is the possible PC version of this remaster, found on the PEGI and ESRB website, entities responsible for age ratings in Europe and North America, respectively.
Atlus has not yet announced a PC version, and in Japan, Shin Megami Tensei III: Nocturne HD has been released for PS4 and Switch, the only official versions announced for the West. However, the plan appears to include the PC version.