Would I be facing any kind of trouble in the future for leaving my degrees incomplete? I have dropped out of 2 MSc in CSE programs because of my health issues and lack of proper math background.
You can check the full story from my previous question.

What should I do now to go ahead and restart my aspirations to become an appropriate candidate for a Ph.D. program?

Now, I am facing a new decision dilemma.
One of the professors from the Faculty of Life Science of a university in eastern Europe just hired me to work with him on a project. The project I would be working on is related to data science and algorithm development. He is also interested in taking me as a Ph.D. student under him. I can start a Ph.D. under him in 2022 if I agree.
Suppose, I enroll and complete my Ph.D. under him. Would I be facing any kind of trouble in the future for leaving my 2 previous MScs incomplete? I have been having a lifelong ambition in working in academia in the USA. Would any problem arise in the future regarding these 2 incomplete MScs?
Another question is, how would it look like if I want to work as a teacher in the Faculty of Engineering in the USA, but have a Ph.D. from the Faculty of Life Science?
Leaving the masters unfinished isn't a huge problem. But moving from a Life Sciences Doctorate to Engineering is a big step and would need a lot of justification. You don't say which university in Europe so it is hard to guess at their reputation.
I won't predict that it is impossible, but I think you will have a hard time convincing people unless you have produces some substantial papers that are pretty technical.
Is getting an engineering doctorate in Europe an option for you instead of one in life sciences? Or some sort of joint degree.
Tough road. Uphill all the way, I think.