How badly will my future job prospects be affected after having my PhD graduation date extended by more than 3 years (due to health)?
It will probably have very little effect. Most jobs / grants / fellowships / etc that are time-limited for early career researchers,


Are based on time since submission or graduation, and pay no
attention to when you started; 
Allow you to argue for longer if
there has been documented sickness (as well as maternity, and some
other things)


The time taken might raise eyebrows on a CV, and if you are worried about not getting as far as interviews because of it you could consider mentioning in covering letters, but "I took longer because I was ill. Now I'm better" is a perfectly reasonable explanation that no sensible person will hold against you.
(if you can't say "Now I'm better", that may unfortunately be a different matter)