OP, this is not the 'right' answer - just my own opinion/experience.
I could have sent my children to nursery at that age, and I didn't. I couldn't see any benefit to it at all. I was with my children every waking minute at that age, and while it turned out to be career suicide for me (which is a different topic), it was absolutely the best thing for all of us at the time.
At toddler groups etc, I could always tell which children were at home full time. They were more articulate, for one thing. They also knew that they had a completely reliable anchor point (namely their parent - mostly mums, but there were a few SAHDs too).
I thought about it a fair bit when they were little, and I remember thinking that there was more to 'socialising' than doing it exclusively with your peers. My children were all very well socialised with people of all ages - not just other toddlers - because I took them out and about to the shops, the library, to visit neighbours, etc, etc, etc.
There was also a kind of symbiosis between parent and child which defies definition. I could tell within seconds that something was wrong with one of mine, just because their breathing was a bit different. If they were coming down with something, they had a very slightly different smell. And so on.
All that said, the afternoons sometimes felt several years long. But that was about me, not about them.
My first one didn't go to nursery school at all. The others went for a couple of mornings a week when they turned three, because I thought they would enjoy something a bit 'extra'. I wouldn't have sent them for full days, though.
Even despite my career suicide, subsequent divorce, penury etc, I wouldn't change any of that for anything in the world. If a fairy godmother came along and said I could be someone else for a day, I would choose a thousand percent to be myself when my children were small.
However... this is just me. It suited our family, but it might not suit others. 20 years ago, I would have said my way was the right way. Now, though, I would say the only right way is what works for you.