Should have taken things a little slower here and verified the pom.
So, I was missing spring-boot-starter-jdbc and I included the following as per the docs:
camunda.bpm.database.type=postgres
spring.datasource.url=jdbc:postgresql://localhost:5432/camunda
spring.datasource.username=???
spring.datasource.password=???
spring.datasource.driver-class-name=org.postgresql.Driver
#camunda.bpm.database.schema-update=create-drop
camunda.bpm.database.table-prefix=camunda.
Seems to be working well.