We asked our paediatrician to hold the diagnosis (He was a totally cut and dried diagnosis case) because DH wasn't sure he wanted DS (then 9/10) to walk through life with a label. DH and DS are very very similar.
The difference being that DS is disabled by his autism - it causes him day to day difficulty in doing things that are considered essential (social interaction, decision making, situational awareness, behavioural regulation).
We decided (as a result of continued issues at school) to go ahead. I came out the other end feeling a bit like you - I've got a piece of paper, now what? Well, kind of nothing and kind of everything.
DS is no less autistic because of his diagnosis.
His day to day life still has challenges far in excess of many of his peers. He has had no specific medical support.
What it has done is give him a language to understand himself and a sense of belonging to some abstract tribe (he doesn't want to hang out with them - he just likes that there are others out there).
It's given us the ammunition we need to get what we need from his school - support, reasonable adjustments, understanding, an arse kicking for the weasel children who try to bully him. It is a shortcut for new adults, clubs, activities etc to understand his need for individual needs assessments.
It's a weird thing, an ASD diagnosis and it took me a couple of years to feel that we did the right thing. Now I have no regrets - there are no downsides for our DS.
In terms of sharing with family, do it in your own time. Not everyone is going to cover themselves in glory and some people are going to surprise you on the upside. Take your time to work out what you want people to do/not do, how it relates to your child/their life/behaviour, so that you position the fact that your child has ASD to them where they're less likely to be shit (looking at you DPIL).