I wonder how can I manage permission/groups to hide every property with personal information such as telephone number, date of birth, etc. for my colleague's accounts(they should not see each other's profile personal information property)?
If I understood correctly, you would like to hide properties from other team members??
If that is correct, taking a look, you could accomplish this from within properties settings by clicking the checkbox next to a property's name > then click Assign Users & teams to select the users/teams that would be able to see the property (this doc details this further). That said, it looks like in order to do this, your account would need an enterprise level subscription.