Yes, Microsoft is bringing back the thin client, and business users will be able to use their existing PCs as one. Cloud PC will run Windows and will be powered by Azure, just as you'd expect, and it's based on Windows Virtual Desktop.
Pricing is different though, as the job listing promises a flat, per-user price. That implies that Microsoft will probably offer Cloud PC as a set, all-you-can-eat subscription service. This is as opposed to the Windows Virtual Desktop pricing that currently exists, and is based on how much resources you consume while using it.
The description in the job listing is as follows:
"Microsoft’s vision of Cloud PC is that it is the only M365 powered user compute experience delivered from azure and managed by Microsoft - at a flat per user price. Microsoft Cloud PC is a strategic, new offering that is built on top of Windows Virtual Desktop to delivering Desktop as a Service. At its core, Cloud PC provides business customers a modern, elastic, cloud-based Windows experience and will allow organizations to stay current in a more simplistic and scalable manner. It has never been a more exciting time for us to start this initiative!"
As for when it will arrive, it's reportedly coming next spring. Perhaps, it could be something that could launch around the timeframe of Build 2021.