First of all, thanks a lot to Martin Decker for his comment and the description how he could solve that problem. Tried that, but unfortunately, these changes alone did not help. I opened a SR and got a recommendation how to solve the problem, exactly designed for my environment. Beside the tasks Martin described, I had to edit some libraries in the directory tree <OMS_HOME>/inventory/featuresets/.
I asked Oracle Support if I'm allowed to publish the solution, but they said:
"We are still waiting for bug fix for a permanent solution and the workaround may or may not suitable for all situations where upgrade option not available. There are chances like inventory details missing also can cause the similar issue hence its better to log a new request if there are any concerns to verify the install logs/screens and provide solution/workaround"
So, in case You face the 'missing update option, too, please log a Service Request using the keywords "Bug 28350114 : EM 13.3 Upgrade, Installation Types Screen Is Not Showing the Upgrade Option" and supply the install logs.
I asked Oracle Support if I'm allowed to publish the solution, but they said:
"We are still waiting for bug fix for a permanent solution and the workaround may or may not suitable for all situations where upgrade option not available. There are chances like inventory details missing also can cause the similar issue hence its better to log a new request if there are any concerns to verify the install logs/screens and provide solution/workaround"
So, in case You face the 'missing update option, too, please log a Service Request using the keywords "Bug 28350114 : EM 13.3 Upgrade, Installation Types Screen Is Not Showing the Upgrade Option" and supply the install logs.