Hello Markus,
Out of the box, Odoo filters shipping methods natively by geography (countries/states) or website, but it does not have a standard checkbox to filter shipping methods by the customer's VAT field.
If you don't want to buy third-party apps or write heavy backend code, you can use Automation Rules  to tag customers as "B2B" when they provide a VAT number, and then use Odoo's native B2B settings.
Let me know if you need any help regarding this
Thanks