UX playbooks are great but they should also be flexible - Over time you will learn new things that require you to change the way you research, evaluate, and design.
Your playbook needs to allow for change - It should never be set in stone - This of it as a toolbox: Every now and then you'll find that you don't have the right tool for a particular job so you'll find the right tool and add it to the toolbox. Similarly, there will be times when the tools you have are actually stopping you from doing a job the right way so you'll need to get rid of them.
Having a playbook is better than having no playbook.
My approach would be to convince your leader of the necessity to keep re-evaluating the playbook on a specific cadence (say once every six months) to see what's working and what's not. Then just fill this first iteration with whatever is needed to get it up and running.
If in six months' time, there is a demonstrable need for considerations about accessibility, task flow, Cognitive bias, UX Writing and so on, then you can start to add those things based on how important they are to your current needs.
BTW: I personally believe that good accessibility provision IS the foundation of good UX.