Do all open source projects have an open-source software steward?
No. Most open source projects will not have a steward.
A steward must be a "legal person" (Article 3(14)), such as a company, and most open source projects are not supported by a company.
The stewarding organization must also have "the purpose or objective of systematically providing support on a sustained basis" (Article 3(14)) and their software must be "ultimately intended for commercial activities" (Recital 19). Organizations who do not meet those tests will also not be considered stewards.
Disclaimer
Disclaimer: The information contained in this FAQ is of a general nature only and is not intended to address the specific circumstances of any particular individual or entity. It is not necessarily comprehensive, complete, accurate, or up to date. It does not constitute professional or legal advice. If you need specific advice, you should consult a suitably qualified professional.