With this project is difficult to suggest a safe and compliant system. Whilst I am familiar with regulations for mobile catering vans, static market stalls are a new area for me. Even where a catering vehicle has correctly installed electrical equipment, it still needs an electrical test and certification by a professional.
Putting together a diy portable battery/inverter will not be independently tested or certificated. I can forsee issues with the various market organisations forbidding the use of such DIY equipment .
Perhaps a way forward is to consider one of the self contained power stations, such as a Bluetti AC 200.
Sorry i cannot be more specific regarding a DIY system