To think some parents overpraise their children to compensate for their own insecurities?

No, I don't think so. If there is any link between an insecure parent and a tendancy to over praise, its more likely to be due to not wanting history to repeat itself. Insecurity is often rooted in how we ourselves are treated as children. So an adult who was raised in a way that didn't lead to self worth and self confidence may well try to do things differently with their own children.

My children know I think they are the most amazing, beautiful people to ever have walked this earth. Of course they know this doesn’t mean everyone else think this. They know I am their mum and slightly biased.

I think you may be misunderstanding praise, OP. Virtually none of the parents who are praising their children think they're raising a mini-Mozart or Cezanne or whatever, they're just being encouraging and interested.

I was a child who was never praised at home (my parents both left school at 13 and tried to get me to leave as soon as I legally could, saying university was only for rich people, and 'not for the likes of us' and suspicious of good marks as likely to attract resentment from my peers and make me not 'stay in my lane.'

I was an adult before I discovered that I was actually clever, and had been clever all along. I'm raising my own child differently.

i think my child is the amazing and beautiful, the best ever. I also expect others to think that about theirs.
As a dyslexic child I would have liked some encouragement.

"My parents never praised me or encouraged me" that's a wee bit sad, from my pov, @Friendlygingercat

"It was not until I went into the workplace that I discovered I had a talent for passing my professional exams"

Just look how proud you are now and rightly so, you are actually special, after all, despite your parents' lack of encouragement?

Over praising is not the way to instill confidence. When the child who is over praised in primary reaches secondary (or possibly grammar school) they will find that there are brighter and more talented kids. They then settle at the middle of the class - a good average - and this can come as a real ego shock. Rather than convincing your little prince or princess that they are a miniature genius it would be far better to model the virtues of resilliance and hard work.

As a child I was top of my class in several subjects but around the middle of the group in others. My parents never praised me or encouraged me to think of myself other than average. It was not until I went into the workplace that I discovered I had a talent for passing my professional exams.

or are trying to be encouraging and instil confidence? 🤷🏼‍♀️

Most parents think their kids are absolutely amazing don't they?

It's not an ego thing, it's a hyping your child up and genuinely thinking they are amazing thing.

I think most parents think their dc are amazing/gorgeous/talented etc it’s surely the point of reproducing! The difficulty arises when that belief crosses over to assuming everyone thinks similar of your dc!