Is there a way to add a new SPWeb (Subsite) via PnPPowerShell (or any other way?) with a site script? I am aware of applying a site script AFTER the creation, but this will cause some unnecessary ootb libraries/notebooks/etc. to be created, rather than just what I need (-> whats in the sitescript).
If you need to do this with a Site Script, you can use the Trigger Flow verb, which can call an Azure Automation PowerShell runbook with PnP PowerShell cmdlets installed which can then use the above cmdlets to delete the unnecessary lists and navigation nodes:
Be aware that Site Designs and Site Scripts do not work well with sub sites. Sub sites are kind of a "faux pas" in the modern world. If you try to create a subsite, there are many scenarios where the site script will not work (for example, site content types and columns are known to not deploy on subsites)