My employer is a european company.
They are contracted to deliver service, that I deliver in Canada.
That requires me to have a work permit, but all applications for a work permit seam to require a canadian employer, that I don't have.

Can a foreign company apply for the service canada confirmation?

What confuses me is that i read everywhere something about entering the local labour market, but I don't do that. I don't intend to apply for a job with any canadian company in canada.

What is the nature of the service being provided in Canada? Assuming that you are providing the service to a Canadian company (e.g., a client of the European company), then that Canadian company is the employer of record for the purpose of seeking the work permit.

The nature of the service is consulting around a product from the european company. The canadian company is buying the product and I support the implementation of the product. I do not get directives from the canadian company. They don't pay for my services directly, but my services are bundled into the product.
Employer of record means to me that the canadian company actually pays my salary, which is inappropriate.
Some of my tasks I just do for the european company and they have nothing to do with any canadian company. So my salary is not fully related to the work for this client. I am just close to the client since it is our biggest client and we want to have a person close by to show our dedication to the client.