Should I include a short summary of my MS research in the Statement of Purpose for PhD position? I am writing a Statement of Purpose (SOP) for a Ph.D. position and confused if I should add a summary of my MS research work. My MS research work is very much related to the advertised Ph.D. project.

I googled it and found that in some SOPs people have written a short summary of their previous work but in others, they have not.
Yes, absolutely.

A statement of purpose for a PhD should indicate why you want to do research and that you are prepared for it. There is no better way to establish that than to discuss your research experience.

However, when discussing your prior research make sure not to only focus on the past. For example, explain how your prior research has motivated you to do more research in the future (via a PhD).