I also have using this feature on my long range to do list AND I have a bunch of old Chromecast dongles sitting in the back of a cupboard no longer in use...
I'm going to suggest that trying to combine non-Apple technology (e.g. Chromecast) with iOS is always going to be a challenge (one of the many reasons I've always avoided the Apple ecosystem), and so getting a cheap/2nd hand/refurbished/older generation Apple TV is likely the path of least resistance...
That said, it does seem possible to use Chromecast on iOS, but the app seems to have to support it, otherwise the only opther option appears to be to Chromecast the entire screen. If that's what you want, then you might be in luck.
There seems to be plenty of articles and videos on the internet on how to do this - just search "Chromecast from iPad".
E.g. https://robotpoweredhome.com/chromecast-from-ipad/
Do share your experience! Good Luck!