You can tile the are being this in front of the door and prevent damage like scuff marks and scratches from the shoes and debris which get stuck to them.

Or just run the floor through and put molding around edges.

My line of work (rehabbing apartment complexes) that threshold would be considered a trip hazard and would have to be dealt with. We are not allowed anything grater than 1/2" in height from the floor..

Tile that section and if codes do not need to be followed. Continue the floor as you are and maybe a piece of 1/4 round to make the height difference not so noticeable.

@Mule you must be in California I think they have a max height of 3/4" and 1/2" for sliding doors

Most places Per IRC code: Landings or floors at the required egress doors shall not be more than 1 ½ inches lower than the top of the threshold. Exception: The exterior landing or floor shall not be more than 7 ¾” inches below the top of the threshold provided the door does not swing over the landing or floor.

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GN

WV..

".. dwelling unit exterior sliding doors can have a threshold height of up to 3/4", and all other doors shall be 1/2" max. Without beveling or edge treatment thresholds .."