Not really, natural gas has immense exposure to geopolitics and the commodity markets: https://www.iea.org/commentaries/what-drives-natural-gas-pri...
There’s also the argument to be made (this has manifested in other countries) that as gas usage wanes and more homes electrify, nat gas costs will increase as the infrastructure costs are spread among fewer and fewer people
This has kinda wonky incentives though - if your fixed costs for gas are high but your marginal costs remain low and for whatever logistical reasons you can't cut the gas connection entirely, then your motivations are to move as much of your heating load over to gas as possible.
This is the kind of thing where a carbon tax is great for sorting out the pricing to match the externalities.
Heat pump water heaters pull heat from the outside. Usually with a split outdoor unit, just like normal A/C and heat pump systems.
I’ve also seen models where the entire system (integrated storage cylinder for the heated water) is installed outdoors, but those are presumably meant for more mild climates.
In any case, they certainly don’t pull heat from inside the house.
AFAIK, the US has a mid-long outlook of gas oversupply. EU's market is broken and has 3x the price (c.f. Henry Hub v. TTF). I haven't seen any major forecasters predict reaching parity anytime soon. Hence, LNG export projects keep getting (over-)built to chase the arbitrage.