Does sky130b allow us to build a SONOS-enabled flip-flop standard cell to store a few bits across a power cycle in a fully digital design?

Yes, you can build SONOS devices (in sky130a or sky130b). The problem is that there is very limited information about the nature of SONOS programming, and no open source IP for the programming and read/write circuitry. There have been a few experiments with SONOS driver circuits on some of the MPW runs. I haven't heard about any results.

Thanks for the answer, Tim. I have some further questions. 1. I've found Bryce Readyhough's spiking neuron design (mpw1 slot4). Were there more? 2. Do we have good enough models to design the read/write circuits using simulation only or do we need some fabrication runs to get them right? 3. Are SONOS devices included in the test tiles A7 & C5? If yes, can we get some useful info out of them? 4. Do I get it right that in order to store bits in a nonvolatile way I need to use either SONOS which is available in both sky130a&b or ReRAM which is sky130b only? I see way more designs using ReRAM, is that the preferred way to do nonvolatile storage?