@Jyri Annunen , since the Microsoft Q&A community has a policy that the question author cannot accept their own answer. They can only accept answers by others, I'll convert my initial comment to an answer in case you'd like to Accept the answer.
Just confirm you're using Create Web App + Database in the following manner?
On the Review + Create screen, you will notice the networking information. Towards the bottom, select Download as a template.
The conflict is with the template trying to create a private link record (
privatelink.mysql.database.azure.com-dblink) where it already exists. I can't correlate what you already have versus what you're trying to create, but it could be VNet association with the private link endpoint, or private link endpoint name for the database, or something else.
What I advise is on the template screen, after you click Download as a template, click redeploy, and check the values prepopulated in the template against your existing VNet and Private Link associations.