The Witcher 4 is definitely happening, but it's likely still quite far away.
There isn't a release date, or even release year yet. The Witcher 4 was first confirmed in March 2022, with CDPR saying "no further details regarding the game—such as a development time frame or release date—are available."
Nope, or at least CDPR says that it's "not planning on making the game exclusive to one storefront." The studio also owns GOG, so it would be odd if The Witcher 4 weren't available there.
Based on which Witcher 3 ending you chose, there are definite possibilities to continue Ciri's story, especially as the 'best' ending sees her return to the Witcher path with Geralt.
Co-founder Marcin Iwinski has stated CDPR sees the first three games as a standalone trilogy. "The Witcher was designed as a trilogy and a trilogy cannot have a fourth part, can it?" So is looks like the number 4 is out.
The teaser image for the next Witcher game is the biggest hint we have to work with. CDPR has confirmed it is indeed a Lynx, rather than a medallion from the Cat school we all know.
Alongside confirmation of The Witcher 4's development, CDPR also explained that it had partnered with Epic Games to use Unreal 5 for the game. It looks like it's curtains for the REDengine.