It really depends on you/the child/the party or play-date, and WHO is giving it.
Some parties will say, drop off party.
Some will say it is up to you or you can stay.
So ask the host.
At this age, it is common to also stay at the party.... but ask the host.
My daughter is now 8... and parties per her age group... parties are either drop-off or you can stay. Once a Host of the party did say it was drop-off only, because per her budget, (it was at a kids venue/entertainment place), she could NOT afford to ALSO order lunch for all the parents. So... she designated the party as drop-off only. Or parents could pay for their own lunch....
so there is that scenario too.
For me, parties are hosted by people I know.... parents I know. So they will always say, that we can drop-off or stay. We all know each other and the kids.
And I also go by my child.... and their cues.
Some kids are fine just being dropped off, some are not.
So... whether it is a play date or party... ASK the Host.
There is no one certain age... by which you 'have to' either drop off or stay there.
For me, when I have play-dates for my kids at our home... I tell the Moms they can stay or leave. BUT.... because my play-dates are for several kids.... at one time, I ask that at least 1 Mom stay.... just for my sanity.
Per parties, and if it is designated as a drop-off only party... the Hosts of the parties my kids attended... then ALSO made SURE.... there were an adequate number of "Adults/relatives" who were there to also properly SUPERVISE all the kids.
When my daughter has been at a drop-off party... or play-date... I ALSO talk to her about it prior, and prep her. I tell her... to ALWAYS make sure she is not alone anywhere and stays with her friend. In pairs. I tell her... to NEVER go wandering away by herself... or to the bathroom... to ALWAYS tell the Adult/Host... of any needs/bathroom/help she needs. To SPEAK up. My daughter... is safe.... in behavior and wise that way... so she knows, what is appropriate or not. I ALSO make sure... she, from a younger age, KNOWS our phone numbers... AND I also give the Host... our contact phone numbers/cell numbers, just in case... AND when I will return to pick her up. Even if early.
And for these drop-off type parties/play-dates... I ALSO talk to the Host... and ask about how many kids are attending, supervision... and about the venue it is being held at.
BUT... usually, my daughter/son attends things with people I know, anyway. And trust.
Otherwise, I stay... at the party or play-date.
all the best,
Susan