Is the covid-19 vaccine-induced copy of the protein spike also damaging cells?
The spike proteins expressed by cells that take up mRNA or ChAdOx vaccines are modified so they cannot induce membrane fusion. However, the research article you refer to indicates that circulating spike protein damages endothelial cells simply by binding ACE2, which suggests vaccine derived spike protein could still cause this kind of damage if it enters the bloodstream somehow:

we show that S protein alone can damage vascular endothelial cells (ECs) by downregulating ACE2 and consequently inhibiting mitochondrial function.

Spike protein is necessarily attached to a membrane, so for it to damage cells by binding ACE2, bits of membrane containing the spike would need to be exported from the cells. The SARS-CoV-2 genes that allow it to do this in a real infection are not present in the vaccines, of course. The only other route I know of by which S protein could theoretically enter the blood is in exosomes. This article analyzed circulating exosomes from COVID patients and did not detect any viral proteins:

We did not identify viral proteins via the purification of exosomes; thus, we can conclude that viral particles were not purified together with exosomes

Research creating hybrid S-protein that can make spike-coated exosomes indicates the natural spike protein does not get into exosomes:

the S protein could not be detected in the sample from pSwt-transfected cells. In contrast, the SGTM protein could be detected in the pelleted supernatant of pSGTM-transfected cells.

I was not able to find any studies looking for spike protein in exosomes of vaccinated people, but it should be less likely than for the actual virus.