Global methods

I start by going to the beforeAll() hook and adding a spy on the console.log method using the vi.spyOn() utility:
beforeAll(() => {
  vi.spyOn(console, 'log').mockImplementation(() => {})
})
I'm overriding the implementation of console.log for this test suite by using .mockImplementation() and providing it an empty function. With this, I can still assert on the console.log calls without it actually printing anything to the terminal output.
From this moment forward, all console.log calls are recorded and I can assert on them in any test!
Next, I need to make sure that the recorded state of spy function is reset between the tests. I will use vi.resetAllMocks() for that:
afterEach(() => {
  vi.resetAllMocks()
})
vi.resetAllMocks() targets all mocks created in this test suite, not just the spy for console.log. Instead of resetting an individual spy, I prefer resetting all mocks because none of them should leak their state to irrelevant tests.
And, finally, restore the original implementation of console.log once the tests are done:
afterAll(() => {
  vi.restoreAllMocks()
})
This concludes the testing setup changes but we still have some assertions to adjust.
Since I am spying on the global method, I can write assertions on that global method directly:
expect(console.log).toHaveBeenCalledWith(
  'Sever is listening at http://127.0.0.1/',
)
expect(console.log).toHaveBeenCalledOnce()
expect(console.log).toHaveBeenCalledWith(
  'Sever is listening at http://127.0.0.1:5639/',
)
expect(console.log).toHaveBeenCalledOnce()
The only thing remaining is to run the tests and make sure they are passing:
 βœ“ print-server-url.test.ts (2)
   βœ“ prints the server message for url with host and no port
   βœ“ prints the server message for url with host and port

Bonus: Type-safe global spies

Although Vitest reassigns the value of console.log to a spy function on runtime, TypeScript doesn't know about that. In fact, if you attempt to read some of the spy function's properties, you'll be greeted with a type error:
console.log.mock.calls
// Property 'mock' does not exist on type '...'
To fix this, you need to extend the type of Console['log'] in your test and mark it as a mock instance.
import { MockInstance } from 'vitest'

declare namespace console {
  var log: Console['log'] &
    MockInstance<Parameters<Console['log']>, ReturnType<Console['log']>>
}
console.log.mock.calls
// [["Server is listening at http://localhost:5639/"]]
The way you extend the global type will depend on the declaration for that type. The type of console.log happened to be declared in a global namespace console so that's the namespace we extend above. Inspect the type declaration of the global you wish to extend to know how to properly do so.