Microsoft are looking at putting datacenters under the ocean

Um, no they're not. That article you linked is from 2018, and the experiment concluded in 2020. They pulled the data center out, and concluded that whilst the experiment was successful, several challenges still remain (such as around repairs and maintenance, physical security and energy supply reliability), so they haven't toyed around with the idea since then.

Basically, Microsoft have no plans at all currently to put data centers under the ocean - unless you've got some insider knowledge.

The amount of heat we would put in the ocean from this would be like pouring a cup of hot water into one of the great lakes. This isn't a issue and would be better for the environment as we are not using all these power hungry ways to cool them.

Arthur C. Clarke wrote a sequel to the sequel to the sequel of 2001 (called 3001) where Frank Poole is rescued a thousand years after been lost in orbit around Jupiter/Saturn. By then global warming isn't caused by carbon dioxide or methane or even water vapor. It's from 1,000+ years of waste heat generated by each human that's ever lived. Even with 100% clean energy, everything still creates heat, and it has to go somewhere.

What specific environmental problems are you foreseeing? I looked through the article and nothing seems troublesome to me.

They were talking about this years ago and I haven't heard anything on it in a while. Is it still even a project they're working on? Also, what would be the environmental problems with this? I remember reading at one point about submarine power cables potentially causing issues with marine animals because of EMF, but I don't think that was any kind of conclusive study.