why won't my canon MG4250 connect?

The Canon MG4250 is mentioned in About AirPrint - Apple Support as a model supporting the driverless AirPrint technology. This means that it can be used without drivers when connected to a network. This is the supported way for macOS Big Sur. See also the guide at https://www.canon-europe.com/support/consumer_products/apple_airprint_guide/ .

If necessary, try resetting the printing system and re-adding the printer (as an AirPrint printer).

Reset the Mac printing system to solve a problem - Apple Support

Add a printer on Mac - Apple Support

It would probably be correct to assume that you are using a Wi-Fi router. Make sure that the printer and the computer are connected to the same network. If so, you may want to try the following procedure: Power off the router, the printer, the computer (and all other devices/computers). Wait two to three minutes. Power on the router. Wait another two to three minutes. Power on the printer. Wait a minute or two. Finally, power on the computer (and all other devices/computers).

Pleas can you tell me where i will find the model number.

The router will have a label on the bottom usually.. out of sight. All products must have a label stating model number but it could be something like BTHome and you don't recognise it.

Its strange if i connect my laptop and printer to my personal phone hotspot it will print it just won't print when connected via the wifi.

OK.. that is helpful to know.

Most modern routers have auto band select. This is often problematic.

Let me suggest you set the router so you have separate names for 2.4ghz and 5ghz bands.

Use simple alphanumeric only names.. e.g. BT24 and BT5. Both can use same password which is >8 purely alphanumeric characters.

Now connect the printer to the BT router.. which will likely use the 2.4ghz band as mentioned.

Connect your computer to the BT router and also use 2.4ghz not 5ghz.. and check the printers again to see if the printer is available.

Tell us if that helps..

... if it fails there is another way to setup the printer. It involves using IP of the printer so I need to know a lot more details including model number of the router...

A simpler solution you may need to use a different wifi AP.. at least for the time being.. this can be a cheap and simple second hand airport extreme or express. Occasionally Apple stuff does not work with 3rd party products.. and since it was Big Sur that killed it.. then the issue is changes made by Big Sur.

It is difficult if an engineer cannot fix it.

Did the printer work after you updated to Big Sur or is that when it failed?

I presume you are using a BT router. Please tell us the model number..

We can try and help but unless you are using an Airport router we are not really going to be able to help much. You are better posting in the Big Sur area.. as it is a computer or network issue.

Addendum

Canon MG4250 appears to be using 2.4 GHz only.