CPanel or Managed Word Press

Based on the Feature list on their website :
https://ca.godaddy.com/help/what-is-managed-wordpress-8926
no, you will not be in over your head.

The managed hosting that you have includes an SSL for your site, but you could apply that on your own in CPanel. I have no idea idea if GoDaddy includes this in the other hosting plans or not.

It’s easy to do – I expect if you happen to stay with hosting at GoDaddy that they will move you at no cost anyway – but ya never know with GoDaddy!

I assume they are referring to this ?
https://ca.godaddy.com/hosting/web-hosting

Also, imo there is simply not enough information in your original post in order to troubleshoot properly and say for certain that this change will work anyway.
It would help more to see the actual errors from your console :
https://developers.google.com/web/tools/chrome-devtools/console/log

Hello there!

You can actually already check out cPanel as they have a demo that you can try out.

If this link doesn’t work for you I would suggest just doing a Google search for cPanel Demo yourself.

https://demo.cpanel.net:2083/cpsess8275254256/frontend/paper_lantern/index.html?login=1&post_login=41609094337034

Hope this helps and kindest regards! :]