The space station's orbit has been adjusted continuously over its lifetime initially by attaching a shuttle to it and doing a burn of the shuttle's engines and later doing the same with progress modules.
My bet is the original expectation of the designers was to deorbit by attaching centaurs (or whatever) to the existing docking ports and rotate the beast to the right attitude for a deorbit burn.
NASA has more recently said they want the reentry to be as steep as possible to minimize the size of the debris field, and is using that to justify the development of a new specialized deorbit vehicle. No doubt SpaceX will declare that Starship is the proper vehicle for this, and then will plow the $800 million into the Starship program. The money they got for Artemus is already long gone and Starship has failed to demonstrate key components of the Artemus plan. Dear Moon has been cancelled so NASA and Artemus are the only customers they have left. NASA knows that without a cash injection Artemus is at risk.
One of Starship's engines on the lowest setting would tear the station apart. Regardless of whether they make this based on Starship instead of something more reasonably sized like a Dragon or Falcon 2nd stage, it'll still need either a new engine design or a big cluster of Dracos. It'll be something custom.
Regarding their Artemis work- the payments are milestone based, so they get money as they pass milestones. Engine relights and ship to ship prop transfer are some of the next ones.
Regarding their other customers- the Starship manifest includes another moon cruise, several satellite launches, and a lot of Starlinks.
It is been a plan for a while in the USA to shift launches from government run to private run for over a decade. This is just an implementation of that strategy.
Longer - fifteen, closer to twenty years. It took this long for there to be one or two companies that they could be sure wouldn't just cut and run (especially given how cutthroat the aerospace industry is).
They have had a plan for it, from the very beginning. Big-budget space projects like ISS don't get anywhere without a wrap-up plan. ISS is in LEO, and its mass contraindicates moving it into a graveyard orbit. Conventionally, stuff in LEO gets de-orbited; same thing happened with Skylab in '79.
Wait, how is Starship failing? They successfully returned from re-entry and made a soft landing with both the booster and starship itself. Seems to me that it's well on track?