The project will not save without a lead status
Dolibarr requires a lead status when creating a project because a checkbox is ticked by default. Just untick it. Verified in 23.
You create a project — a building job, a deal, a case — and Dolibarr requires a “Lead status”: Prospection, Qualification, Proposal, Negotiation, Won, Lost. This sales vocabulary makes no sense for what you do, and yet it is impossible to save without choosing.
The cause
On the creation form, the “Follow opportunity” checkbox is ticked by default. As long as it is, Dolibarr considers your project to be an ongoing sales deal, and the lead status becomes mandatory.
The solution
Untick “Follow opportunity” before saving. The project is created without asking for a status. Nothing else to change, no setting to modify.
How this was verified
On a Dolibarr 23 test instance: with the checkbox ticked, the status is required; unticked, the project is created normally. The project was created, checked, then deleted. It is a thirty-second test, but it is the difference between a reliable answer and a guess.
If you never want to see this checkbox again
Lead tracking is part of the sales side of the Projects module. If you do not use it — as is the case for many organisations that manage building jobs or activities, not a sales funnel — it is cleaner to configure the module once and for all, so that the screens only ask for what you actually use.
More generally: in Dolibarr, a mandatory field whose purpose you do not understand is almost always the consequence of a checkbox ticked somewhere else. Look for the checkbox before looking for the workaround.