No, the driveway wouldn't count. Texas doesn't define burglary by property boundaries; you have to enter a "building" or a "habitation", and a habitation must be a "structure" or a "vehicle".
Are you sure that doesn't qualify on the basis that it is the curtilage of your home? Often this counts as "in your dwelling" because it's in your private space that immediately accompanies the dwelling.
I think this has applied in the case of self defense in Texas, at least on someone’s porch. Curtilage is a general concept, not specific to the fourth amendment.
> Arguably, the protections contained in the [self-defense] statute include what is referred to in legal parlance as the “curtilage” of the property (a home’s porch, steps, garage, or yard)
But the reasoning is, specifically, that defending yourself against someone who is in the curtilage must be protected, because defending yourself against someone who is "attempting to enter" your habitation is protected, and it's impossible to attempt to enter the habitation without being in the curtilage.
This is not compatible with your analysis, which assumes that a person present in the curtilage has already entered the habitation.
In 2021, Kyle Carruth shot someone on his porch and used a castle doctrine argument in his defense, and he was not indicted. That would suggest that the porch is considered part of the habitation separate from an attempt to enter. I think the thing you are citing as an authority here is the opinion of a law firm and not a case, and not necessarily a good one (law firms run the gamut from "alcohol addict in a strip mall" to big law).