How get started with drupal10 on localhost?

I'm trying to prototype a drupal10 site on a macOS localhost, where I already have apache and mysql installed and running. I already used:

composer create-project drupal/recommended-project ~/Sites/mysite

To /etc/hosts, I added:

127.0.0.1   mysite.local

I'll add modules and a theme later.

But what, exactly do I do next to access and begin adding content to the drupal10 site?

The many and varied sources of documentation, including the INSTALL.txt file, are quite confusing and even seemingly contradictory as to what else needs to be done.

What, exactly do I do next to access and begin adding content to the drupal10 site?

Docs say that the drupal installer creates the mysql database, but exactly what exactly do I need to do further to "install" the site and thereby to have the database created.

And what url do I use? I tried mysite.local, but apache does not find such a site.

Please be explicit (and gentle!).

Answering your questions:

What, exactly do I do next to access and begin adding content to the drupal10 site?
If your installation log (that long text on yout terminal, after you type the composer command) don't show any errors you need to create a database to your Drupal website:

https://www.drupal.org/docs/installing-drupal/step-3-create-a-database

After the creation of the database, you need to configure your installation and after that you can run the installer. On your browser access: /core/install.php

And what url do I use?
Have you tryed access http://mysite.local?

You see, as you said that's the URL you have point your enviroment, "telling" to apache point your localhost to this URL.

This is the official Drupal guide:
https://www.drupal.org/docs/getting-started/installing-drupal

But if you prefer, I have a suggestion that will make your life a lot easier. Use Lando:

https://docs.lando.dev/drupal/getting-started.html

It will create a virtual machine, much easier to configure and use.