Paleontology has been really helped by the ease of sequencing, to the point where many evolutionary arguments are moot. Humans are apes, birds are dinosaurs. Some people still dispute it, but not with evidence on their side.
I particularly like this Futurama clip on the subject. https://m.youtube.com/watch?v=VzGtk7Ip4NU
Not that I doubt that, but how does DNA help, when we have no DNA samples from dinosaurs?
But you're right, it is the fossil record that provides the strongest evidence.
Saying that birds have the same DNA as birds is not evidence of much of anything. :)
Eg here's a nice paper discussing Bayesian phylo combined with rexord sampling. https://www.cambridge.org/core/journals/paleobiology/article...
I'm in an adjacent field so take it with a grain of salt.