PhD from Sikkim Professional University

As for Phd from Sikkim Proffessional University will give an good opportunity and also boost your C.V weightage.

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.
(Private University)
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.

Sikkim Manipal university is a private university having its recognition from UGC. However, in respect of its NAAC accreditation, it could not be confirmed. This university is offering numerous courses and all such courses are at par with the courses of the other recognised universities in respect of recognition of UGC and their NAAC accreditation.
Hence you can safely undertake your Ph.D course from the said university and in no way, it will pose any problem while pursuing your jobs or otherwise.

You can join Sikkim professional university for obtaining PhD degree. As It is a private university but UGC approved. It is established in 2008 as per the act SPU (Act No. 11 of 2008) of Sikkim State Assembly. There would not be any problem in making a career in this field. For more information, you can go through the UGC website where you will find state wise list of UGC approved universities. whether it is NAAC accredited or not, that is not mentioned on the website.

Sikkim Manipal University is a famous university that is also recognized. Provides not only regular but also private courses and this gives full recognition to your degree in other fields after studies. As you mentioned, if you have an offer from Already University, then you must definitely adopt this offer. If you want, once you can get more information regarding admission etc. from its website.

Ph.D. is an important degree in which not only is limited to theory but you also have to write a thesis for it and also have to work a lot on projects etc. important for. There are very good institutes available for Ph.D. not only in the country but also in the world and it is a study whose level is also very high.

As you have discussed in your question that you are more interested in the government sector for the job, you need to understand that the value of a Ph.D. degree is measured in terms of knowledge and skills. That is why not only knowledge but also your skill development is important. After Ph.D., there are more chances of jobs in the following areas -
A college professor in a Government college.
Consultant Positions in Government Sectors.
Industrial R&D Lab Professionals and
Start-ups Mentors in Industrial Research and Development Organizations

As the Sikkim Professional university is a UGC approved institution you can very well go ahead with your PhD programme. The point here is that for getting a job or good position in the busines and industrial environment today PhD is not the only thing and what matters is your earlier academic qualifications and your skills for working in a particular industry or organisation. So I would sugest you to go ahead with your PhD also and that would give you an edge for getting jobs like lecturership in educational institutes but for entring in the industries you will have to acquire some certificate or diploma in a niche area which can add value to your PhD qualification.
You have not mentioned your subject that you had in your UG/PG levels but nowadays there are many professional short term courses that are job oriented in their nature and help the graduates/postgraduates/doctoral degree holders immensely. So consider those options also alongwith your pursuing the PhD programme.