Basement – Hydronic radiant heat in ceiling

After checking what type of instant water heater that is - since it's gas-fired, your operating cost will be MUCH lower with gas providing the heat than with electric resistance heat. Perhaps 30% (not 30% less, unless you have remarkably low electric rates and high gas rates) - typically near 30% of the cost of running electric resistance heat, for the same heat output.

Electric can be a shade thinner, but it's on the order of 1/4" .vs. 1/2". In either case, you should build an insulated floor on the slab unless the carport slab was insulated (very unlikley) or you'll be trying to heat the outdoors via an uninsulated slab, so the effective difference in height is none, really. Depending what you want for a floor, lay 2" XPS (extruded polystyrene insulation) and embed your tubes in gypsum cement or something like that on top of it, or buy pre-grooved subflooring to drop tubes into (and then pay attention where not to drive nails, or just don't choose a nailed down flooring.) There are a number of common systems for adding radiant heat on top of an existing floor.

Your goals are somewhat at odds. Even where radiant floor heating is used as the only source of heat, the floor typically does not get anywhere near "toasty." The floor temp is typically only 5 to 10 degrees above ambient (75 to 80 F), and the vast size of the radiator (i.e. the entire floor) provides enough energy to heat the entire space with such a small differential. So, the floor will feel better than an unheated floor, but since it is still colder than your body temp, it won't feel "toasty" by any means. So, if you piped enough energy into your floors to make them feel warm under foot, you'd likely overheat the house!

The only "toasty" floors I've experienced is a heated bathroom floor. In that case, there was electric coils under the tile (several hundred watts worth for a large bathroom), and indeed, the floor felt warm underfoot.