But does the text not entail at 2:19 that the animals were created just before Adam named them?

That would pose a problem insofar as the birds were made on a previous day, the fifth. But this is no problem; the situation is very similar to that noted above, regarding 1:4: these are just a few small details needed to contextualize the account of Adam and his activity. There is no need to insist rigidly that the birds and land animals were created just before Adam named them. The point, rather, is that in God’s natural economy, in his design, they were created for man, who by naming them, exercised dominion over them (cf. Gen 1:26-28).