Is a Yongnuo YN560-TX radio transmitter compatible with a Canon SL3/250D or T100/4000D?
No. Those cameras, along with a few other recent low end offerings from Canon, do not have an ISO compliant hot shoe with a trigger pin in the center to tell a non-TTL flash to "fire." The YN560-TX is not capable of receiving a "fire" signal from a camera that does not have a center pin.
The only workaround for using manual flash with these cameras missing the center pin would be to use manual power mode with an E-TTL compatible flash with firmware making it capable of operating without the center pin. Or you could use an E-TTL capable trigger that works without the center pin on the hot shoe. The flash would either need to be capable of receiving the signal from the trigger OR attached to a receiver capable of receiving the signal from the trigger OR directly attached to the trigger if it had a passthrough hot shoe with a center pin that would be activated by the trigger based on the signals from the camera via the TTL contacts (as opposed to a "dumb" passthrough shoe).
Your simplest solution would be to purchase an E-TTL capable flash that can work without the center pin. In addition to Canon's own E-TTL flashes, there are at least a few E-TTL capable third party flashes that can do this with the latest firmware versions installed. Godox has released firmware updates for at least one wireless radio trigger and for three flashes that will allow them to work with at least some of the cameras¹ with the borked hot shoe. Godox products are also marketed under various "house brand" names such as Adorama's Flashpoint in the U.S. as well as several "in-house" nameplates in Europe and elsewhere.
For off camera flashes, you only need a trigger compatible with the pin-less cameras and flashes compatible with the trigger.
This is where Godox (and associated brands) really shine. Godex's 2.4Ghz "X" system triggers can control everything from their cheapest manual only flashes all the way up to their biggest TTL studio monolights and all recently released products in between.
Yongnuo, on the other hand, has separate radio protocols for their manual only flash system (YN560/RF605/RF603) and their TTL flash system (YN622). While most of the recent TTL flashes can receive instructions from the manual only triggers, the manual only flashes cannot receive instructions from TTL triggers.
My advice would be to look at a Godox 2.4Ghz 'X' trigger and whatever Godox flash fits your needs. If you want to start with only on-camera flash, then get a Godox TTL capable flash that can be used on the hot shoes missing the center pin. This should provide a solution for at least the T100/4000D if not the SL3/250D.¹
You could use off camera flashes capable of reacting to the camera's built in flash. This is called "dumb" slave mode. You'll probably need a flash with "S1" and "S2" capability. S1 fires on the first detected flash of bright light. S2 ignores the first detected bright flash of light (which is the camera's pre-flash used for automatic TTL flash metering or red-eye reduction) and hopefully fires on the main flash pulse from the camera's built-in flash.
Radio vs. Optical
Optically controlled remote flash is fast becoming old technology, though. Radio has a number of advantages over optical communication. Among them:
- Distance limitations. Most optical systems, especially when using a weak built-in popup flash or a near-infrared unit as the controller, are much more range limited than radio systems. Radio tends to have a greater range, especially in bright light.
- Positioning limitations. Most of the optical controllers only cover an area about as wide as a 24mm lens on a FF camera. If the remote flash, or remote receiver on the camera, is further to the right or left of this cone it may not receive any optical signal, even if it is only a few feet from the transmitter! Radios transmit in all directions from the camera or remote trigger.
- Line-of-sight requirements. In addition to being in the "cone" of light transmitted by the master (or remote when triggering a camera remotely), off camera flashes and the receivers on remote cameras must have a clear line-of-sight to the master with the optical receiver pointed in the direction of the master. This inhibits being able to place optically controlled flashes inside modifiers, placing them behind objects in the scene, placing a remote camera out of line of sight of the trigger, etc. Radio systems are not limited to line-of-sight and can even be used on the other side of walls and other obstructions (although the obstructions may reduce the range somewhat).
Difficulty with bright ambient light. Especially outside under sunlight, the power of optical wireless control is very limited. Again, especially with a relatively weak built-in popup flash or a near-infrared transmitter, the master just doesn't have much power to cut through the bright sunlight and the receivers can't detect the weak signal from the master over the very bright sunlight. Radios work just as well in bright sunlight as they do in a dark studio.
Multiple Photographers. Radio has the ability for more than one set of the same type to be used in proximity to one another without interfering with each other. (Think several press photographers all using Canon covering an event for multiple publishers. Or more than one shooter at a wedding.)
¹ Most of the Godox firmware updates list all of the Canon cameras with the crippled hot shoe except the SL3/250D. I assumed that this was because the firmware updates were released before the SL3/250D was introduced. But there have been reports that even units with the latest firmware do not currently work with the SL3/250D. Godox may be able to provide further firmware updates in the future to make their devices work with the SL3/250D, or they might not.