java.lang.IllegalArgumentException: No PersistenceProvider specified in EntityManagerFactory configuration

Change the emf bean configuration and add a new bean called jpaVendorAdapter:

<bean class="org.springframework.orm.jpa.LocalContainerEntityManagerFactoryBean" id="emf">
  <property name="packagesToScan" value="com.medsoft.stadto.entity" />
  <property name="dataSource" ref="dataSource" />
  <property name="jpaVendorAdapter" ref="jpaVendorAdapter"/>
  <property name="persistenceUnitName" value="stadto"/>
  <property name="jpaProperties">
    <props>
      <prop key="hibernate.show_sql">true</prop>
      <prop key="hibernate.hbm2ddl.auto">create</prop>
    </props>
  </property>
</bean>

<bean id="jpaVendorAdapter" class="org.springframework.orm.jpa.vendor.HibernateJpaVendorAdapter">
  <property name="showSql" value="true"/>
  <property name="generateDdl" value="true"/>
  <property name="databasePlatform" value="org.hibernate.dialect.PostgreSQLDialect"/>
</bean>

Also make sure you have a persistence.xml in the META-INF directory:

<?xml version="1.0"?>
<persistence xmlns="http://xmlns.jcp.org/xml/ns/persistence"
  xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
  xsi:schemaLocation="http://xmlns.jcp.org/xml/ns/persistence
  http://xmlns.jcp.org/xml/ns/persistence/persistence_2_1.xsd"
  version="2.1">
  <persistence-unit name="stadto">
    //No need to specify the provider as we already have specified JPA vendor in applicationContext.xml
  </persistence-unit>
</persistence>

It happens when you don't configure JpaVendorImplementation for JPA. The below Java bean definition for JPA EntityManager works for me:

@Bean
public LocalContainerEntityManagerFactoryBean entityManagerFactory(
        DataSource dataSource) {
    LocalContainerEntityManagerFactoryBean emf = new LocalContainerEntityManagerFactoryBean();
    emf.setDataSource(dataSource);
    emf.setPackagesToScan(irdbConfig.getPathForPackagesToScan());
    emf.setJpaVendorAdapter(new HibernateJpaVendorAdapter());
    emf.setJpaPropertyMap(irdbConfig.getAdditionalHibernateProperties());
    return emf;
}

But the below one throws same exception you received:

@Bean
public LocalContainerEntityManagerFactoryBean entityManagerFactory(
        DataSource dataSource) {
    LocalContainerEntityManagerFactoryBean emf = new LocalContainerEntityManagerFactoryBean();
    emf.setDataSource(dataSource);
    emf.setPackagesToScan(irdbConfig.getPathForPackagesToScan());        
    return emf;
}

Please notice the lines which are removed from the second code.