Bill by the hour, with no budget.
Leave the budget empty and a project is hourly. Its value is the hours you log times your rate, and the calendar adds up the week's value as you go. The advisory calls above have 9h 30m logged at €70, which is €665 of work.
With no budget there is nothing to run over, so the project shows no budget health. This works on Free, at your default rate. If you want a limit, add an hour budget, also on Free, and Phased shows the hours left.