I took a look at the mbed os socket API, and it supports opening a socket in 'listen' mode. With a few lines of code, you should be able to build this into a basic server. What functionality is missing that would be required for the use cases you mention?
mbed's documentation is an absolute mess, with islands of information and little to no linking to relevant places. I had been looking at their mbed client api -- https://docs.mbed.com/docs/mbed-client-guide/en/latest/ -- which only supports client -> their server activities, and doesn't link at all to the lower level APIs. The socket support they provide is also a lot more limited than other RTOSes that target Arm Cortex-M devices, for example TI RTOS and NXP's MQX both offer IPv4, and full IPv6.
Then again, it seems to typify a lot of ARM's software offerings. They have Keil uVision, which is an Eclipse-based IDE, that is barely mentioned at all in the various mbed documentation, and doesn't have any integration with their newer toolchain they seem to be building up. It just gives a very unfocused feeling in general regarding using their toolings.
Relevant link: https://docs.mbed.com/docs/arm-ipv66lowpan-stack/en/latest/1...