Ensure rubber gym floor is flush to floorboards in hallway?

Hi there, looking to have a gym in a new build.
Planning to install some sort of rubber mat flooring (on concrete)
i.e. Asking the builder to not do floorboards in the gym and to just leave the concrete

To cope with the different levels (to be safe) - I've asked for a sliding door (I was worried that a hinged door would not swing properly if the floors are level to begin with). Or is there a good way to do this and keep it hinged?

But also in general I'm now thinking how do I make sure the rubber gym flooring is as flush as possible to the hallway?

Yet to ask the builder, but want to check what flooring is under the sliding door?

Any thoughts - no idea what exactly to do and what is normally done?

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