I didn't look at the details of how they sequenced it, but given that there are chemically modified bases in the mRNA vaccines there is a chance the normal methods for sequencing (and the first step of translating to DNA) don't work. Well, I guess in practice they did.

While not completely equal to the naturally occuring bases, the modified bases in the vaccine mRNA need to be able to complement to the non-modified ones present in tRNA anticodons during translation. If they can pair to their corresponding natural bases, then the chemically modified RNA can be also used as a template by the reverse transcriptase to generate the complementary DNA needed for the sequencing reaction.

Generally I agree, but it could be the case that the modified bases work just well enough for tRNA matching in the ribosome, but not with the reverse transcriptase.

The mechanism of base complementarity is identical in both cases. If a modified uracil complements an adenine in tRNA, it will complement an adenine in the RT primer or an adenine being added to it.