Update: I found the issue.
First of all, I realize that the links I provided in the OP are expired which probably explains why nobody is able to help me.
Nevertheless, LatencyMon reported storahci.sys as the culprit whenever I had audio pops and high dpc on that driver.
I have 4 drives on my PC:
1 x M2 NVME
1 x SATA 3 HDD
1 x SATA 3 SSD 120GB (Corsair)
1 x SATA 3 SSD 250GB (Samsung)
I realized recently that the Samsung SSD wasn't detected anymore (I don't use it much so I didn't notice immediately) but didn't connect it to the audio stuttering.
I unplugged all SATA drives = no more high dpc on storahci.sys.
I plugged just the Samsung = issue is back
I plugged all SATA drives except the Samsung = issue disappears
And all this time, the Samsung drive is not detected.