Funny how only the Chinese financially sponsored this research you're talking about, despite the fact that the paper has some American co-authors. Anyway, it's the dose that makes the poison. This research may been published in good faith, but its findings have been used by anti-vaxxers out of context.
Downregulation of some ACE2 receptors, which is what the paper claims (in its title), isn't that big of a deal unless it happens at large scale. The study itself says that
vaccination-generated antibody and/or exogenous antibody against S protein not only protects the host from SARS-CoV-2 infectivity but also inhibits S protein-imposed endothelial injury.
In other words, they concede the condition is probably self-limiting in the immunocompetent.
Following [Moderna] mRNA vaccination (which has the highest dose of mRNA among the approved mRNA vaccines), levels of spike protein in the blood have generally too low to detect except by "ultrasensitive single-molecule array (Simoa) assays" and more importantly (with rare exceptions) anti-bodies cleared the spikes from blood in a few days, following the 1st dose, and from everyone in the test group a couple of days after the 2nd dose.
S1 antigen was detected as early as day 1 postvaccination, and peak levels were detected on average 5 days after the first injection.
The mean spike peak level was 62 pg/mL ± 13 pg/mL. After the second vaccine dose, no S1 or spike was detectable, and both antigens remained undetectable through day 56. For one individual (participant 8), spike was detected at day 29, 1 day after the second injection and was undetectable 2 days later.
Alas the latter paper lacks a comparison basis with what's detected following actual infections with SARS-CoV-2. Anyway, in correspondence to the press the lead author of this latter study concluded that
“We found that within a few days of the antigen appearing, the individuals developed antibodies that removed the antigen from the bloodstream,” he added. “Our conclusion was that the vaccine is working as intended.”
In other words, it's not a real clinical concern in most people. I'm not like totally dissing these findings, as they might be related to the myocarditis side effect of mRNA vaccines, but the fact that the latter most often happened after the 2nd dose suggests it's not the spike directly that's involved in that one.
By the way, "damages some [heart] cells" is true of bare mRNA (vaccine) released into the bloodstream as well, in animal models and in sufficient dose, at least in terms of detected inflammatory response. (For what's that worth, a co-author of this latter study is "the inventor [of] an intranasal influenza vectored SARS-CoV-2", i.e. no injection needed.)