Versions published while Pro is active can continue running commercially after your subscription expires. Needle branding does not reappear in those already published builds: the license is verified when you upload or deploy and remains valid for that version.
You need an active Pro subscription again when making changes or publishing an update. The same licensing rules apply whether you host the project on your own server or on Needle Cloud.
Needle Cloud storage limits and paid hosting features are separate from the published version's license and depend on your current plan.