Once you take it apart, you’re unlikely to be able to buy new wheels. Better to replace the whole unit - I did this just last week with an office chair.

Pull the entire black part out of the gray part but don’t throw it away yet. Bring the old castors to the hardware store to check the size and shape when you buy new castors. In Australia, new ones are sold like this:

https://www.bunnings.com.au/move-it-50mm-black-hooded-office-chair-castor-2-pack_p3940114

You should be able to find something similar where you are.

The amount of work (parts, tools and time) required to do a good job repairing that isn’t worth it. Just buy a whole new caster wheel.

go to a big box store. go to the metal bar stock section- usually they’re in the pick-and-choose nuts and bolts area. Alternatively, just ask. (I like local hardware stores, they’'ll have it too, somewhere. better selection of pick-and-choose hardware, too.)

Get some smooth rod slightly smaller in diameter than the rod there. use the rod to knock it out- either in a press (if you have access to one) or by setting it in some kind of clamp and pounding on the rod with a hammer.

if their only options for bar stock are expensive, you can get a bolt that’s also slightly undersized and use that.

for the record, the wheel looks like it’s an absolute gonner, so you’re probably going to have to get more parts anyhow.

I would expect that the wheel shaft has a flange or maybe some knurling on it to prevent it from coming loose. You will probably need to drill it out. I wish you the best of luck on your journey, you will learn a lot about how things are made. I also expect that this will end with you buying a new castor or a new suitcase.

I suspect a press is your best option, which is really a slightly more controlled variation of your hammering it with a screwdriver effort.

Drill it out. Start with say a 2.5 mill and go up in size until the metal is gone

I assume the metal axis is probably molten firmly into the plastics with some kind of knurling. So probably you are going to break the plastics if you are trying to push it through. As suggested by others, a solution may be to try to drill it out. The other option I see, is to remove the whole black part and replace it by new rollers with have standardized shafts.

I don’t have an answer, but I can smell the grease from here.