TNT's C-Band feed usually stops the side by side and has full screen ads and promos during the designated local ad breaks. They are also the ones who trigger the local ad breaks via cue tones that are sent to the C-Band receivers at every provider's headend, so it's also happening at the same time on Comcast, Spectrum, Dish, FiOS, YouTubeTV, etc.
The commercial break at 7:53pm ET was all full screen, with national ads for Arby's and Harbor Freight, promos for some HBO shows and TNT Sports when the local break was triggered, and then a national ad for Breztri after the local ad break ended before they returned to the race at around 7:56pm ET.
If local ads were being triggered at other times and covering up the side by side, that's likely a screwup by Turner/WBD as the avail notice for NASCAR they sent out says that the local breaks are only supposed to trigger between stages.