For all Starter plan environments and Pro plan Integration environment, you can allocate more space for MySQL in the .magento/services.yaml file, by increasing the mysql: disk: parameter. For example:
mysql:
type: mysql:10.0
disk: 2048
See the Set up MySQL service article for reference.
To make these changes for the Staging or Production environment of the Pro plan, you must create a Support ticket. But typically, you will not have to deal with this on Staging/Production of the Pro plan, cause Magento monitors these parameters for you, and alerts you and/or takes actions, according to the contract.
Applying the changes
Once you change the .magento/services.yaml file, you need to commit and push your changes, for them to be applied. The push will trigger the deployment process.