A vaccine causing long-covid and a vaccine possibly aggravating an already perturbed immune system, potentially contributing to altered RBC behavior ie, being "sticky" are pretty different outcomes. I think the latter is more plausible than the former.
The spike protein present in the blood during an actual COVID infection is thousands of times higher than the spike protein fragments that make it into the blood after vaccination. In fact, at first, it was thought that spike protein didn't make it into the blood from the vaccines, but a
May 2021 paper using an "ultrasensitive single-molecule array" showed extremely small amounts of the S1 fragment of the spike protein on days 1-7 after the first moderna vaccine injection, but not after the second, presumably because the immune system clears it. Basically, if you keep lowering the detection limit on your testing, eventually you will find something, but personally, I don't think it is enough to cause a problem. I think the more likely scenario would for vaccine reactions is stirring up the immune response.