Full stack means you write code running on back end and front end. 99% of the time the code you write on the FE interfaces with your other code for the BE. It’s pretty coherent and feedback loops are similar.
Devops/SRE on the other hand is very different and I agree we shouldn’t expect software developers be mixing in SRE in their day to day. The skills, tools, mindset, feedback loop, and stress levels are too different.
If you’re not doing simple monoliths then you need a dedicated devops/SRE team.