Sikkim Professional University is a private institution founded in the year 2008 as per the act SPU (Act No. 11 of 2008) of Sikkim State Assembly. University Grants Commission of India (UGC) has given the recognition. The university is having recognition from the Indian Nursing Council (INC) and the Pharmacy Council of India (PCI) also. Their website is https://www.spu.ac/.
I have checked the UGC official site and found that this university is having UGC approval. You can also verify by going through the website of UGC. https://www.ugc.ac.in/. On this website, there is a State-wise List of Private Universities as of 06.08.2021. In that list, this college is there at Serial Number 317.
Sikkim Professional University (Formerly Vinayaka Missions
Sikkim University), Plot No. 438, N-312 Sang Phatak Road,
Middle Tadong, PO Daragaorn, Tadong, East Sikkim – 237 102.
Name Changed w.e.f 23.10.2020. This is the description given in that list.
So you need not worry about the recognition of the University.
But there is no mention of the NAAC accreditation. The reviews about the institute are good by some students.