Yes, except for AAV (Adeno-associated virus) which has a unique ITR (inverted terminal repeat) structure at the ends of the DNA that facilitate extrachromosomal survival of the DNA.
Fair enough; but the relevance of the reverse transcriptase is to provide a putative mechanism for instructions from mRNA to make it into the genome, under specific circumstances.
Whether it happens in conjunction with the jab, I don’t know; but to assert the possibility is not indicative merely of abysmal ignorance which conflates DNA with RNA or supposes them to be freely interchangeable.