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.