If they do repair the engine, is there any extended warranty offered on it? I wouldn’t expect the warranty extension to apply to anything else but you might try to get a longer warranty on the engine.
Yes, to fix this right the engine will need to be essentially rebuilt, especially the bottom end. I don’t know if the valves/head will need any service but I am sure it will be inspected as that must come off for this work. You might offer to pay for a new head or a rework of this head if that isn’t included. That may be overkill though as this isn’t really the issue with your car. On the other hand, the oil burning may have gummed up the valves.
The important thing is that you are keeping an eye on the oil level. The engine can go a lot longer with an owner like yourself vs. some that just run them low until they lock up hard. I have known people who use the low oil pressure light as an indicator to add oil and this usually doesn’t end well for them. One guy would carry a quart with him and pull over and add the quart when the oil light came on. He never even checked the level but would only add a quart but I am sure he was still low at this point.