The mRNA and spike proteins may have a short half life. Neither I nor the reference I provided not the reference you provided contradict that point.
The polyethylene glycol coated nanoparticles are PROTECTIVE CARRIERS of the mRNA. It is THOSE that are are resistant to breakdown or excretion. That’s their main purpose ... to resist breakdown or excretion so the mRNA can continue to be exposed to cells for an extended period of time.
Once those PEG coated nanoparticles are in you, they are likely there for life, similar to, for example, the ink particles in a tattoo. The reference you provided includes this line: “Vaccines mostly remain near the site of injection (the arm muscle) and local lymph nodes.”
Even if the nanoparticles do eventually break away from whatever local tissue they attach to and make it to the general or main lymphatic circulation, the key point remains: the PEG coating blocks biochemical and hepatic breakdown, and the nanoparticles are too big to go through the kidneys. Sure, there’s GI excretion and respiratory exhalation, and maybe even sweat ... nut none of those are likely to be significant means of excretion of these nanoparticles. Like a tattoo (prior to the advent of laser tattoo breakup) one you have those nanoparticles, you, as certain as anything can be in biology, you have them for life.
The nanoparticles themselves may have some minor toxicity, but that’s a different topic. It’s the nanoparticle contents mRNA) that are biologically active and thus going to have effects until those contents run out. The time for that running out to end is unknown.
I tried.
Believe whatever nonsense floats your boat.