I don't think it implies anything shady; non-legal is not illegal. A non-legal entity, as far as I can tell, is simply an entity of some kind that is not a legal entity, that is, not endowed with legal personality, not able to enter into contracts. It can be a trade name, or a grouping of legal entities that is not a legal entity in itself; see here:
"The Governance of Non‐Legal Entities
An exploration into the challenges facing collaborative, multistakeholder enterprises that are hosted by institutions"
https://www.iisd.org/sites/default/files/publications/govern...(The IISD, International Institute for Sustainable Development, is a Canadian organisation)
I don't think it's an exact synonym of unincorporated, though its meaning may depend on the jurisdiction, as AllegroTrans has said. I think something can be a legal entity without being incorporated.
As far as I can see "non-legal" always goes with "entity". You don't describe a company as "non-legal", for example; you say it's a "non-legal entity" (if it is).