Deploy website to IIS from linux build agent

Question

Problem description

I have a jenkins master that uses a linux build agent to build my ASP.NET Core websites using official MS linux docker containers.

I previously used a windows VM with the necessary tooling installed to build these projects and used MSDeploy.exe to deploy the sites to an IIS webserver. For this deployment I created a web package.

In my linux docker container I obviously can't use MSDeploy.exe.

Question

How can I savely deploy an ASP.NET Core website to an IIS webserver from a linux docker container?

MSDeploy.exe connects to the IIS using a local IIS Users credentials, shutsdown the app, replaces all files that are also present in the new package, so it not just replaces the files but also does some safety settings around the actual replacement.

Misc

I've found this question here, but unfortunately no real answer was found there.

Thanks in advance