Congratulations!
have 6 DC aged 16, 14, 10, 7, 5, 5. The first 4 were planned, the twins more of an accident. I love having a big family. I agree that 4 is definitely when you see people start to take notice, count etc. Comments-wise, I think you just have to ignore or try and make a joke of it.
When my youngest was born, I had 3 under 2, so 4 under 6. Yes it is chaotic and yes it is tiring but there are so many moments too which make it fun or funny or rewarding.
TBH I don't think the jump up from 3 to 4 was that difficult compared to the other jumps
You're gonna have to start planning everything like food, taking here and there, etc and it will still feel a bit like mayhem half the time, but you just get on with it.
When people say they couldn't cope I usually think 'yes you could' You just cope with the circumstances that are thrown at you. When I only had 2 kids I found it just as difficult and would've probably been amazed at someone with 6 kids too but when it happens to you just get on with it.
But don't be afraid to ask for help, babysitting, etc if/when you need it.
Sorry I don't have any experience of homeschooling, but I'm sure you can find people here who do if you want advice on that