I'm not sure if there is support for single-precision simulation and code generation of the kind of standalone optimization solvers you are seeking. But there are some optimization solvers embedded inside some other modeling elements that do support single precision simulation and code generation. I don't know if these fit your higher level need, but investigating these MAY lead your efforts in a useful direction.
Model Predictive Control Toolbox provides modeling elements for controls that can be used with double precision or single precision floating-point. Model Predictive Controllers use optimization solvers to determine the plant inputs in real-time.
Using the model from this documented example, the controller can be changed to use single precision and put in its own reference model (R2021a version attached).
This simulates in single precision and still provides the desired closed loop system behavior. The generated code uses only single precision and no double precision. The generated code would be suitable for a embedded controller like a Cortex M4F that has hardware for floating-point singles, but can only support doubles via big and slow software emulation libraries.