The register
The register lists Stayokay Limited in London as a licensed sponsor on Skilled Worker, an entry that goes back to at least 2026. Rating on the current register: Worker (A rating).
Companies House lists it as Stayokay Limited, number 11162617, incorporated 2018: 8 years of filings behind the name. The registered office is at 128 City Road, London, EC1V 2NX, EC1V 2NX. Its filed activity puts it in property.
A licence says an organisation may sponsor; it does not say it is hiring today. The way to find out is the same as for any employer: the careers page, the job boards, and a direct approach with a UK-style CV that says early that sponsorship would be needed.