Technology

As far as I understood it, SpaceX uses the word "orbit" liberally.

No, that's not really right at all. With this last flight they brought the starship above 200km (100km is generally considered the point at which you're in space), so they definitely went much higher than they needed. In low earth orbit, the velocity needed to hold that orbit is about 28000 KM/H, they kept their velocity below 27000 KM/H for safety/responsibility reasons. That way, if something failed and they couldn't relight their engines, it would naturally come down anyway in a predictable manner. The closer you get to actual orbital speeds, the less predictable the re-entry and impact location will be, so 27000 KM/H is really as high as you want to go if you want to ensure predictable re-entry. It looks like they maxed out at 26750 kmh.

Also, after they reached 95% of orbital speeds, we know they still had lots of fuel in the tank because it had enough to slow down and land exactly where they wanted it to. And then... it still had enough to explode in a huge fireball, so clearly the rocket could have gone further. Or to look at it differently, all the propellant mass that got used up in that huge explosion at the end, that could have been payload mass. So clearly it has the capacity to put up a payload as well. I think the reason they haven't yet is that mastering the reusability aspects are just a higher priority than the payload bays, I think we all trust they can design a payload bay when it comes time for that.