Yes, you would have to purchase/get a new esim.

No Canadian carrier (and very few worldwide) supports quick transfer of esims from one iPhone to another.

https://support.apple.com/en-ca/HT209096

That’s  disingenuous. Few indeed support “quick transfer.” However, I’ve only researched a few countries personally for how carriers do eseim transfers, but as far as I can see in general, it’s supporter via an app or accessing your account online. The carriers I have seen support some free method without requiring new payment to swap an existing esim from phone to phone, and indeed the list for that is significantly larger than “quick transfer”. The app options are typically quite seamless and outside of technical definitions, I’d say qualifies as what a layperson would call a quick transfer. 

I sure wish Koodo had a system like my overseas provider.  Naturally,  eSIM is totally free with them and swapping phones is as easy as logging into the app, activating the new SIM and approving the switch on your old phone. 

A three minute process if that, and of course 100% free to encourage usage and combat the plastic soup environmental issues...

For iPhones, when you go into the cellular section, if the carrier supports esim quick transfer you’ll see a screen like the one below to prompt you to transfer over your esim or even convert your physical sim to an esim right in the iPhones menu.
You are right though that other carriers support a way to transfer an esim quickly without using apples official way, my brain just snapped to the “Quick Transfer” function from Apple.

In Canada, the only carrier that I’m aware of that you can easily get a new esim online would be Freedom though, every other Canadian carrier requires the purchase of a new esim/visit to a store. (Hopefully the carriers hop on board with the new tech soon as I find it all a bit silly personally)

Haha yes I know we went off on a little tangent there, but it just baffles my brain that it isn't free and available through self serve. Or, at the very least, a one time purchase tied to your line. 

But as I said, that's going off on a tangent so I'll get off my high horse now