For anyone who finds this and still looking for help, based on the above and following this documentation from Cypress and had to customize it a bit for Task

https://docs.cypress.io/app/tooling/typescript-support#Types-for-Custom-Commands

Ended up with a cypress.d.ts file in my root with the following to dynamically set response types for the specific custom task name and not override all of "task".

declare global {
    namespace Cypress {
        interface Chainable {
            task<E extends string>(
                event: E,
                ...args: any[]
            ): Chainable<
                E extends 'customTaskName'
                    ? CustomResponse
                    : // add more event types here as needed
                      unknown
            >
        }
    }
}

Probably a chance for a cleaner approach if you have a large number of custom tasks, maybe a value map or something of the like. For now i am moving on cause way too much time wasted on this.