I wanted to add to my above post OP.
My mum put unfair pressure on me to mix with people. We were on holiday when I was 13 and I wasn’t socialising. She suddenly said to me when she know no one else could hear, in a very harsh voice:
“Look, me and your father WANT you to make friends. No wonder you’ve got no friends, always on your own, you’re TOTALLY selfish”
I took this to heart, OP, and it made me extremely vulnerable. The ‘selfish’ comment stuck with me, and in the forthcoming years I was bullied and humiliated by some very nasty kids who definitely didn’t have my interests at heart. I went into an abusive relationship at 18 with someone I didn’t love. It resulted in heartbreak - but he’s happy now.
But anyway, the wider context to my own situation was that I was an only child and mum back to work full time straight after I was born. Ok, nothing objectively wrong with either of those things. However, there was something wrong with this - my mum was sadly an abusuve alcoholic. Why this is relevant to the general situation you describe OP is that because of my personal circumstances I HAD to be self reliant and happy in my own company. - I was often lonely because my mum was knee deep in gin - but had to just get on with it. I didn’t really want or need the company of other kids.
I think 13 year old kids generally are much too infantilised and are much more capable/mature than people give them credit for. My grandad was working full time when he was your DD’s age and had left school! At 13 I was ready to leave school and get a job but the school leaving age at the time was 16.
if kids are natural loners - I think this is absolutely fine ! Thing is, as an adult no one has the authority to coerce people into relationships - so why would people do it to children ?
The other thing I was thinking about yesterday was - it’s ok to have no friends at 13 because at that age, you don’t realistically ‘choose’ your school, and your wider community, your social circle or anything. For instance, at 13 I was at a school whose demographic overall I really didn’t like. By 23/33/43 - you’re much more likely to genuinely be choosing circles you mix in as you have more power/leverage.
Just to clarify I’m making my own GENERAL observations above, OP, I’m in no way implying that your parenting of your DD is wrong in any way !