Confirmed there was ongoing paperwork for my dog too, though the rhythm was less frequent than the initial import process. Worth checking your own destination’s specifics though, not universal.
We got so focused on the import process itself that it didn't occur to me there might be ongoing paperwork afterwards — until a vet mentioned in passing that our dog's documentation needs updating periodically, not just at the point of entry.
Now I'm not sure what's actually a one-time thing versus something recurring I need to calendar in, and the sources I've checked all seem to focus entirely on the initial move rather than what happens in year two, three, and beyond.
For anyone further along than us — is there genuinely ongoing paperwork to stay on top of, and if so, what's the rough rhythm of it? Trying to avoid a situation where we accidentally let something lapse simply because nobody told us it existed in the first place.