I don't know if SkyWarn is even a thing anymore. Last year, the Houston SkyWarn repeater was hosting a net from Oregon as Hurricane Beryl was making landfall.
I used to monitor the local Skywarn nets when severe weather was in or near the local area. Back in the 90's when there was a large area of severe weather locally, I was monitoring when a local chaser, who I knew from high school, was one of the first to spot a large tornado that caused widespread, significant, damage to Desoto & Lancaster, just to my south. (I'm in southern Dallas).
But the net had started to be less useful, as 'old timers' passed on, without active 'new recruits' filling in the gaps. When I gave up utilizing the net, it had pretty much deteriorated to a debate forum, trying to weed out and discourage newcomers, and focusing it towards only long-timers.
Of course the TV channels depend a lot on the personality of the weatherman that suits you.
The local network affiliate stations are active when severe weather is active in the area, or approaching quickly. Several have their own specially equipped 'chase vehicles' that they deploy when a strong storm, or line of storms, is in the region headed this way. A couple of stations have active 'chasers' among their on-camera meteorologists, who may be out in the field when not scheduled to be on-air. Most of the stations have at least a couple of non-employee chasers, associated with the station, who may be filing reports from any area of the region, including far west Texas, or in Oklahoma.
"Fox 4" (KDFW) and WFAA Ch 8 (ABC) have five meteorologists on staff, and when severe weather is predicted, or approaching, at least one of them are in-studio, providing updates,radar tracking, and other details at any time, even early morning hours. If weather is extremely bad, they usually have one or more members of the crew on hand as well, with field reporters feeding video of damage that has occurred.
"NBC 5" (KXAS) has six team members, and is very focused on weather, as a legacy from the (now deceased) locally well known original area personality Harold Taft.
"CBS Texas" (KTVT Ch 11) promotes "First Alert Days" when severe weather is in process or forecasts. They show 3 personalities on their web page, but I think their actual staff is five. They promote a specially equipped 'weather chase truck' that may have some weather monitoring equipment installed.
All of the stations will use a split screen, to include radar along with normal programming, when weather is worsening, going to all-weather, all the time, when a extremely severe storm is in progress.
Me local TV Weather Person live and a pay version Weather App that lets me see several different weather radar scans.
The television streaming app that I use has access to local stations across the US, Canada, and other locations abroad. I can monitor stations in other areas for coverage of breaking events, whether weather or otherwise. Last year, NWS issued an extremely worded severe weather alert for the state of Oklahoma, with potentiate for very are hail and EF-3 or stronger tornadoes likely in much of the state. I set up a couple of Oklahoma City stations to watch, if something broke. If you remember the old 'Stormchasers' series (on Discovery) a couple of years ago, you may remember that an EF5 storm took the life of one of the featured chasers in a storm in the OKC Metro area. Several cities, such as Moore, in the Oklahoma City area, have had more than one EF4 or stronger storm inflict major damage, as well as fatalities.
The OKC stations take their weather very seriously. When 'spot checking' what was happening in their area, one station had their helicopter, as well as a couple of vehicle based chasers, feeding selective video on a strong storm that was over 100 miles west of the metro area. Fortunately for them, that storm did not build to incredible strength, and ended up tracking northeasterly, keeping it out of the immediate metro area.
There are several phone apps, as well as webpages, that feature live storm chasing video from various areas. Of course, it's luck of the draw whether video from your specific area, or one of interest to you, is available.