Not sure what you mean with internal solver.
If you want to interface a new solver, I think a quick way to understand what is needed is to look at the recent commit where Highs was added as a supported solver. As you can see, you have to update definesolvers, sdpsettings, and create one interface file. Nota bene, this whole commit was one-shotted by Claude 4.6 in VS Code copilot with the prompt "Here is the YALMIP repository. Highs can be found in c:\.... Add that solver to YALMIP by integrating it in sdpsetings, definesolvers and writing a suitable interface".
https://github.com/yalmip/YALMIP/commit/908bf2056a5acb0e87cf3e4f219a3029d1bb9040If you really mean internal solver as interfacing other solvers via internal YALMIP calls, I think looking at bnb or bisection or solvebilevel could be useful.