Thank you for your question!

Strawberry clover normally does not do in well in Texas as it is adapted to the Northeastern Part of the United States. The clover we have that is native to Harris County is White Clover.

Yes, you can seed clover into an existing St Augustine lawn. You will not be able to use lawn weed killer which kills broadleaf weeds in a lawn, clover is a broadleaf plant.

Also, clover does not need to be fertilized because bacteria found on the clover's roots has the ability fix nitrogen from the atmosphere. A clover containing lawn will not need to be fertilized like a grass lawn. Clover lawns like regular irrigation once or twice a week when it is hot.

While many people consider white clover to be a weed within their lawns their are benefits of having it present. For example, clover is a favorite pollinator plant for bees and other beneficials.

Keeping it mowed to the lower end of that may help keep it neater and more “lawn-looking,” though it may also interfere with the flowering that attracts bees, so you’ll have to find a balance you’re happy with. Keep in mind that clover readily self-sows, which is helpful when you’re growing it as a crop, but it can also be a little weedy–something to keep an eye on in your flower beds and on the periphery of your yard. Clover does tend to be clumpier and less dense than grass (though white clover is better about this), so it is very often mixed with some grass seed (commonly fescue) instead of grown as a straight 100% field to avoid patchiness.

Clover will tolerate some foot traffic, but I am hesitant to recommend it for heavy traffic areas. It tends to be quite slippery when wet and will crush more easily than turfgrass under prolonged impact.

Here are some interesting articles about planting clovers in lawns:

Should you move over to clover? (colostate.edu)

Is white clover suitable for lawns? - Cooperative Extension: Garden and Yard - University of Maine Cooperative Extension (umaine.edu)