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You could use import in your new stack instead?
<https://www.pulumi.com/docs/guides/adopting/import/>

Once I've imported it, can I remove that reference from the other project without it being deleted when "pulumi up"?

You'll have to do some state "magic" I'd assume.
Export the state to local file, remove the resource, and references, then import the state again.
<https://www.pulumi.com/docs/reference/cli/pulumi_stack_export/>

<@UB39JFCKC> correct me please if I'm talking stupid stuff

there’s a command `pulumi state delete` to do that without messing with the state manually

There is an issue for moving, feel free to comment/upvote <https://github.com/pulumi/pulumi/issues/3389>

when deleting the state, what am I referencing exactly, the pulumi URN?

yes, help for this command has an example

I've upvoted the issue, and recommended that perhaps a recipe of steps in how to move resources between stacks would be very helpful to newbies like myself

Oh cool, didn't know about the `state delete`