eBay stuff is so cheap. Is it in any way safe?
Nope, nope, and heck nope. You got that pic off an eBay listing. It's sold by several sellers.
Everything installed in North America needs to be listed by an NRTL - that is an independent, recognized testing laboratory. Other Federal and state agencies watchdog retail stores to make sure unlisted junk isn't seen on store shelves. However they can't control mail order - that would be Customs' bailiwick and Customs doesn't have the resources to look for drugs, to say nothing of non-UL-listed products. Amazon Fulfillment (which ships many eBay items) is also a big backdoor - no responsible agency has the legal war chest to go after Amazon.
That particular item is being dumped by many sellers who sell them by the dozen, using identical photos. That looks shady to me. I suspect it's a counterfeit, but you could check with Intex to be sure. If you're chasing a name-brand for quality, I think you're barking up the wrong tree.
The fact is, resistance electric heaters are very inexpensive to make. There's no reason one should be costly. You are much better off finding a UL-Listed model. Since you already have a solar heater, you don't need a pump. Even an old water heater would suffice, really. They even sell small, 1-4 gallon water heaters that run on 120V and some are even made to plug in. Plumb that in to replace the solar mat, and Bob's your uncle.
Regardless, GFCI will be mandatory
Anything that powers something poolside will need GFCI protection. With 240V circuits that can only happen at the circuit breaker (EVs being an odd exception).
Fortunately, this beautifully moots ThreePhaseEel's question about 3-prong or 4-prong dryer outlets. 3-prong outlets aren't even safe to use for dryers - turns out deleting ground and tying the dryer chassis to neutral went about as well as you'd expect LOL. But with GFCI involved, even if it is a 3-wire circuit, you can install the 4-prong outlet and connect ground to nothing, marking the outlet "GFCI Protected / No Equipment Ground". That renders your dryer safe and gives you pool-safe 240V power.