There are several articles I've found which seem to anecdotally back up the suggestion that waking up slowly is better than waking up abruptly, in terms of combatting sleep inertia:
https://www.nbcnews.com/better/pop-culture/make-your-day-better-stay-bed-longer-really-ncna837176
https://qz.com/1301170/sleep-inertia-explains-why-you-feel-so-groggy-when-you-wake-up/
https://www.brightontheday.com/4-benefits-of-waking-up-slowly-and-how-to-actually-do-it/
However, I want to know if there have been any studies conducted which directly compared the effects on sleep inertia of waking up slowly and mindfully vs. swiftly and energetically. I wasn't able to find any through Google Scholar.