Is the addition one level or two.? If it is one level I would remove the boards at the bottom. Close in ad brick all of it like the original part of house. Do you really need an outside door on the addition? Removing steps to addition will make back of house and doorway look better.

I doubt you’ll be able to get an exact match to the current brick. So unless your willing to paint or whitewash the whole exterior adding brick might be impractical.

If you are talking about stucco or brick on the top but leaving the skirting on the bottom, I don't think it will have the desired effect.

It is an unusual addition.

You could paint the siding to match the rest of it, since that blends in with the brick. I dont think it looks bad as it is, however.