^ Well that's good news, as that can apparently be invasive here. But, now I'm really clueless about what it might be, then?

It looks a bit like Artemesia dranunculus.

It does. Does it grow wild in Texas?

Hmm, Artemisia dracunculus (Wild Taragon) doesn't ever seem to have lobed leaves, though?

Can you post a photo specifically of those lobed leaves? I'm not seeing any in your already posted ones.

Apparently leaves can be lobed or not.

https://gobotany.nativeplanttrust.org/species/artemisia/dracunculus/

^^ Look at the bottom of this photo, and you can see a lot of the "chicken foot" leaf lobes.

^ Wow, so this might be Wild Tarragon (Artemisia dracunculus)...because in those pics and this one, it even seems to start out with lobed, "chicken foot" leaves when small...and then grow more unlobed leaves as it matures (just like this specimen)!

Seems like it may be a flavorful potherb?

"Tarragon has a flavor and odor profile reminiscent of anise due largely to the presence of estragole, a known carcinogen and teratogen in mice. However, a European Union investigation concluded that the danger of estragole is minimal, even at 100–1,000 times the typical consumption seen in humans."

And although some believe it's native...it seems more likely to have been introduced?

"is native to the other parts of North America"

"Originally thought to be native to Siberia, tarragon now grows wild throughout Eurasia and North America and is cultivated as a culinary herb"

The wild ones usually have no flavor, or unpleasant flavor. If you want good tarragon get a clonal form of French tarragon.

Artemisia ludoviciana

Dubious about ludoviciana. That has silvery foliage and broader leaves in my experience. And the flowers have dark centres. https://www.wildflower.org/plants/result.php?id_plant=arlu