I got a 12 month extension on 30th May and when I landed back in June she was about to stamp me in for 2023, until I told her (very politely!) she was looking at the wrong page. Had a chuckle. Imagine being on overstay the minute you enter the country 😂
They would notice your international arrival and this is different from just visiting another province, for which they said it is not required. I'd say yes, you need one to play it safe.