Confirmed by Deadline, with some added details:
The new season will complete post-production, and the studio will be looking for a new home for Star Trek: Prodigy as season one comes off the service shortly.
The company said that “continues to be invested in growing the Star Trek franchise” with series including Star Trek: Starfleet Academy, movie event Star Trek: Section 31, Star Trek: Strange New Worlds, which returned for its second season June 15 and has been renewed for a third season, animated series Star Trek: Lower Decks, which will return for its fourth season later this year and has also been renewed for a fifth season, the upcoming final season of Star Trek: Discovery as well as Star Trek: Picard.
Update from series writer Aaron J. Waltke:
Obviously, there is not much I can say. Everyone on the cast and crew loves #StarTrekProdigy deeply.
I have noticed some misleading headlines, so all I can do is point to this particular part of the press release.
We are completing season two on schedule and seeking a new home!
Variety's report contains this:
According to an individual with knowledge of the situation, although the show had aired on Nickelodeon in addition to Paramount+, it will not be returning to Nickelodeon either. Those on the show will complete post-production on Season 2 and then CBS Studios will be free to shop it to other outlets.