In any well functioning grid that should all be priced in and batteries will be charging during the cheapest and cleanest times and discharging during the dirtiest and most expensive times.
If externalities were priced into the grid, we basically wouldn't have air pollution.
Since we're talking about Texas apparently most coal plants by kw-h are either offline or in some cases even decommissioned. Apparently in 2023 13.2% of generation was sourced from coal.