im quite deep in the story, will I miss any early story content from the new update?
When characters receive new story events, they are after the previous events, so no you're fine.
Runey has remade some early events, but those are more for upping quality and rewriting dialogue he feels isn't his best, etc.
The only "missing out" is the new early game explore content - you can absolutely still play it on a later save, but it will feel off chronologically (eg characters who know you acting as though they don't), because it was specifically made to make the early game more active.
Yes, without restarting you will miss out on remade content, and newly added story events to the beginning of some character's story. Android specifically has gotten a lot of work done to her early story.
This is why I have a special recommendation for v0.16 to do a fresh install and a new save, though it isn't necessary.