The paper you link to is overexpressing LINE1 on plasmid in HEK293 cells and coinfecting w. sars-cov-2 - not exactly a natural setup! They see some nucleocapsid fragment integration and limited expression, but it's a pretty forced experiment, honestly. Also the whole virus is very different from the mRNA payload of the vaccines. Having a random chunk snagged by an overexpressed retrotransposon is a far cry from a meaningful integration event. Though LINE/Alu transposon integrations are an interesting driver of evolution on million-year timescales.

(and: not a hobby. I was at UCSF, Stanford, and helped start several biotechs. You would have more traction here if you acted a little more thoughtful with those trying to talk to you.)