Technically, all life came from a common ancestor, so if Darwinian evolution follows the same rules in the Pokémon universe, they'd have a common ancestor too. The question is how recent that common ancestor was and if it's a common ancestor of something else.
For instance, in modern taxonomy, there is no common ancestor for carnivorous plants that isn't a common ancestor for all other plants--but there is a more recent common ancestor for tomatoes, potatoes, nightshade, hemlock, chili peppers, eggplant (aubergine), and tobacco, despite them having little in common, and so they're all classified under the family
Solanaceae. (There is an even more recent common ancestor for grass, bamboo, sugarcane, oat, wheat, durum, sorghum, rye, fescue, barley, millet, corn (maize), and rice, and they are a part of
Poaceae.)
It can be assumed, though, that all bird-like Pokémon have a relatively recent common ancestor. The question becomes: Is there an even more recent common ancestor between Doduo and Galarian Zapdos? If you ask me, the closest relative to Galarian Zapdos is Kantonian Zapdos. Both Doduo/Dodrio and Galarian Zapdos are flightless, but there have been instances of birds achieving flight, then losing it through evolution such as chickens, penguins, and kakapos. It may just be a case of convergent evolution. It may seen strange that the woodpecker-derived Pikipek evolves into the toucan-like Toucannon, for example, but they have an extremely recent common ancestor (in geological terms), more so than of birds in general.