I would like to be able to supply external users (customers, potential leads, suppliers) across organisations and internal users inside my organisation with documents. The documents should be organisable per user individually. E.g. Customer A should be able too see documents for the product he bought, not more and not less documents.
No further functionality is currently needed besides that. Is SharePoint the right tool for that job? If not what other tools can you recommend from your experience?
I see you tagged SharePoint 2019, I'd advise against using on-prem SharePoint for Sharing documents externally. It is possible, but to do it securely is complex and expensive. O365 on the other hand is pretty simple and the security is already implemented for you. You can determine the level of access that your external users have and you can extend that by using additional tools provided by Microsoft Information Protection.
You can secure access by forcing guests to login or simply have anonymous links. To add to that you can automate your publishing processes using Power Automate, the O365 workflow.
Take out a trial subscription and make sure it meets all your requirements first.