Good news: this transition is designed to be smooth, with no surprises.
You'll get a heads-up email about 30 days before your child's birthday explaining what's about to change.
On the birthday itself, the account becomes eligible for self-management - your child can start managing their own account where 13 is the local consent age. In some EU countries the digital consent age is higher, so there this happens at 14, 15, or 16 instead.
Turning 13 does not automatically loosen anything. Privacy settings stay at their most-protective defaults:
These only change if your child opts in themselves after taking over the account.