I am thinking of doing Azure certification, but i am not sure if that is the right career path for a DBA.
Up to you. You can look at the cloud side, you can look at the dev side, you can look at the BI side, you can look at the machine learning side, etc. I generally recommend that people get a broad understanding of what's around their field, if for no other reason than when someone comes and asks about 'technology X', you can give them a high level view and you know where to get more information.
Personally, I would say that getting at least familiar with the Cloud side of the DB business is important, you'll likely get inquiries about whether to move databases to one cloud or another, whether to implement new systems in one cloud or another or earthed, about what features of the vendors cloud offerings will be of use to the business (and there are a lot of features and offerings).
On the Azure side, MS has made it clear that they're working cloud-first, new features go into Azure and later into the earthed SQL product (and there are some nice new features coming)
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