Domains like e.g. example.com, example.net and example.org are standardized as example domains, such as for use in e.g. documentation, and, like in your case if you are not actually sharing a real domain name.
This one is the major problem of your set up.
While it isn’t technically impossible to do such things, they would require quite a bit of advanced rules (e.g. on Cloudflare’s side, in this situation).
And, even if it was possible, those kind of advanced routing rules would make it easily to mess up the whole configuration of your inbound flow, which would just be one of many reasons I would expect to be the reason that you’ll typically never (or at least only very rarely, if ever) find providers out there, where this is possible to do.
If you set up a domain with a MX record on that IP, sure?
MX for example.com goes to Cloudflare Email Routing.
Point that email address to send it’s messages from [email protected] to e.g. [email protected].
On spaghetti.example.com, you add it’s MX records to point to the hostname of your actual server.
And, add @spaghetti.example.com as an email alias for @example.com on your actual server, unless you are willing to change your addresses there to be @spaghetti.example.com instead.