Kimai is an open-source time-tracking platform for project-driven teams. It records working hours and analyses them by user, customer, project and activity, and it can create invoices from configurable templates in PDF or DOCX format, as well as e-invoices in XML and PDF/A. It also offers roles and teams, login via LDAP or SAML, a JSON API, plugins, exports to formats such as XLSX and CSV, and support for more than thirty languages. Kimai can be self-hosted, for example with Docker, and is also available as a managed service called Kimai Cloud.
According to the project, the self-hosted version is 100% open source under the AGPL 3, so you keep full control of your data. The privacy policy names an individual in Vienna, Austria, as the responsible party and states that Kimai Cloud runs at Hetzner Online GmbH, with the server location in Falkenstein, Germany. Both the provider and the hosting therefore sit within the EU.