And many commercial airliners are sold without engines at all.

The operators, such as Delta, do not actually own engines on the aircraft they fly, even though they own the aircraft. The engines are rented from e.g. Pratt & Whitney along with a maintenance contract. That said, that engines are in fact installed at the factory.

It’s a requirement that the airframe and engines are sold separately dating back to the original reason why United Airlines was named.

Which is not to say that commercial jets can take any old engine. Even something like this 767 that was split between GE and P&W have specific structures related to the original engine.