Please post photos and measurements.

You need to post pics please . Usually yhe best answer is unfinished flooring same species stained to match not some patternt o draw attention to the fact it does not match

How about an actual rug?

Since you need to replace the actual flooring in front of the sliding door, you really do have three options.

The first option is an expansion of the idea from Norwood. Just put a rug over the area that needs to be replaced. When you are ready to replace everything, do it.

The second is to purchase unfinished flooring of the species and width that you already have. Since you have engineered flooring, you will also want to consider any bevel on the flooring. Get those pieces stained to match and install. If you get the species, width, and color right, you can do it without pulling everything.

The third option is to partially refinish the flooring. Get the color right. It may "show" that there is a patch in the finish, but maybe it won't be too noticeable to anyone else. And if you cover it with a rug, all the more better!

Why does the hardwood flooring near the sliding door need to be changed? Should you explore something other than hardwood to prevent similar damage in the future?

Sounds like you need to fix the flashing on the door. Paying special attention to the header and sill pan flashing. Then install tile. A great patterned tile, done as a rug, is a classic look.

I like the option of tile as shown above. Doesn't have to be that particular design but it would be easy upkeep and could look cool.