How to unit test an old deprecated application

I was assigned the old web applicator (JSF 1.2 + Eclipselink), there is no middleware such as EJB or Spring, and the application service level consists of POJO, which calls EntityManager directly. The code structure looks like this: SomeBean (bean support) → SomeServices (there is a combination of business logic and a data access code), without a separate DAO layer. The code in service classes usually looks like this (very simplified here):

 public void someMethod(SomeEntity someEntity, ....) throws SomeServiceExeption {
    try{
        entitiyManager.getTransaction.begin();
        //lotOfLogicHereAndCallingSomeOtherPrivateMethods
        entitiyManager.getTransaction.commit();
        }catch(Exception e){
            log.error("");
            if(entitiyManager.getTransaction..isActive()){
                entitiyManager.getTransaction.rollback();
            }
        throw new SomeServiceExeption(e);
    }
}

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