My 3 1/2 year old son is very much like this... Playing with me (or his dad or his grandparents or other kids) is always his activity of choice and he really resists doing anything alone. I also very much agree with tangledblue, that it's a personality thing - and that your little boy seems to be just very social by nature... and it's a great idea to think of different ways to satisify his social needs (playdates, local activities, grandparents or other family if nearby, friends of all ages)
In all honesty, I think I would struggle to create a Montessori homeschooling environment for my son for this very reason... It seems to be different at preschool - the higher children to adult ratio, the way the environment is set up plus the examples set by other children in a multi-age classroom seem to naturally support doing things independently in a way I would find quite challenging to reproduce at home. That's not to say it can't be done, but I think adjusting your expectations a little might be key.
Firstly, I think there are two aspects to "independece" here that it might be helpful to consider them separately. Does your son refuse to do things for himself, or does he just refuse to do them alone? Our son is very independent in the first sense - he accesses his own snacks, drinks, art and crafts supplies, is very capable in the kitchen, can clean up spills, change his own clothes, etc. He just doesn't like being alone while doing any of these things! Still, my experience has been that the latter type of independence can be promoting quite effectively, even if you are present most of the time... in our case, just by gentle encouragement and when I did help him, always trying to keep my help to a minimum and resisting taking over to get something done more quickly. And of course, I'm not hovering over him while he's doing any tasks, just remaining available if (or rather when!) he wants my attention.
Of course, being able to do things alone and just "being alone" is an important skill to have in its own right. I think here, IMO, the key is to accept where your child actually *is* at this point in time and try to let go of expectations where you feel he *should* be. So start small, with clear expectations. I've gotten a few suggestions from the teachers at my son's school - one is set a timer, just for 5-10 minutes in the beginning, and explain that you will be unavaible for that amount of time but can do some activity afterwards together. Another idea is to get your son working side by side, but encourage each of you to focus on your own work rather than interact. I'm still working on these, to be honest, but it gives you a few more ideas.
Anyway, very best of luck with your continuing homeschooling adventures. I hope you find a path forward that works for both you and your son.