about the error on Google App Engine we are now aware of it, thanks for reporting. the problem on Google App Engine is this An error has occurred when trying to initialize jsreport.. seems like there is already a server running in port: 8080, basically when running on Google App Engine somehow an env var called PORT is set to 8080, jsreport has some logic that when the PORT env var is defined no matter what it uses that value to bind the jsreport server on that port, so your asp .net core server and your jsreport server is trying to use the same port and that is the reason of the error. we don't have a workaround for this right now but you can keep track of the problem here and know when it is finally resolved.
In the case of running it with docker on linux, Is the dockerfile like this?
i don't have much experience with net core but in this post there are other steps involved in order to setup a good net core image for your app so maybe you can take a look at that and try to run it. after that it should work, as long as you are using that correct jsreport linux binary on your app.