Hi,
Yes, it is possible that there is no recovery partition, as there are so many other recovery options such as Cloud recovery:
https://support.hp.com/us-en/document/c06162205
clean install using Microsoft media (for free)
https://www.microsoft.com/en-us/software-download/windows10
and the various recovery options in Windows 10. The refresh is part of Windows 10 and not HP recovery.
Personally, for a boost in performance, I would replace the 2.5" HDD with a 2.5" SSD such as the Crucial MX500 or similar and reinstall the OS on it. It would give a great boost to everyday performance.
Hope it helps,
David
Please click on thumbs up for thanks
Please click on accept as solution if answered your question