mRNA vaccines don't create circulating spike protein. The specific mechanism of action of mRNA vaccines is to create a spike protein inside a cell (muscle cell - it's an intramuscular injection) which then gets presented by the MHC-proteins on the surface of the cell.

This is a similar mechanism which viral-vector vaccines use as well.

This is quite unlike regular protein-bolus vaccines which do in fact just inject a bunch of antigen into your body.

Of course in all cases, intramuscular injections don't really enter the bloodstream anyway: the immune system picks up the injected material and it is transported by the lymphatic system to be presented to the various immunological systems.

Contrast to general viral infection where a self-replicating virus with machinery specifically intended to ensure it is packaged and secreted from infected as a viable infectious agent will basically run rampant until an immune response mounts...at which pointy our blood actually will be full of pieces of spike protein from your immune system shredding virus particles (which is why PCR tests can detect infection for weeks after you've cleared it).

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8402319/