I'm not very good at discerning noises in those typ of video, but if you don't know when the engine mount was replaced last, it would be a good idea to go ahead and do it.
Here's a good description of the job:
https://www.pelicanparts.com/techarticles/Boxster_Tech/10-ENGINE-Engine_Mounts/10-ENGINE-Engine_Mounts.htm
I recently made a video:
https://youtu.be/h0BQQymTRPs
Also make sure that your power steering fluid is at the correct level and filled with the right fluid: Hydraulic Fluid CHF 202 or equivalent.
Anther 'grinding in turn' noise could be a wheel bearing, but I don't think that having the storage compartment lid open would make any difference in that noise.