Depends a bit on a lot of factors. What is your location, how hot water do you use etc.

I would try as much solar as possible. First thing is reducing needed energy as much as possible. Insulate your tiny well and heat with a mini split (like the panasonic heat charge), in summer these can cool as wel. For cooking I would use induction (I don't like combustion gasses in my house). For hot water I would use a low flow shower head and have short showers. Options for hot water I see are: hot water heat pump, electric boiler, electric tankless, propan tankless. Pro's of a hot water heat pump are: most efficient and can doesn't use a lot of power when running which makes it a good match for solar. Con's are: takes a lot of space, has standby losses, gets heat from the inside which needs to come from your heating system and relative expensive. When hot water usage is low I don't see the point in a tiny. A small electric boiler can be turned on short before showering, this gets problematic if more people want to shower. An electric tankless uses a lot power, however with a low flow shower-head and waste water heat recovery this can be reduced. when a small one is used I expect a small water flow though till the waste water heat recovery kicks in. A propan tankless needs to be installed outside of the tiny (or needs external ventilation) which makes it vulnerable for freezing. I'm still figuring things out myself. Maybe a small electrical boiler and small tankless water heater in series combined with waste water heat recovery. The boiler guaranties a good flow at the start of shower. Once the waste water heat recovery kicks in a small electric tankless has enough power. For dryer I use a heat pump dryer. During the summer months I expect solar to generate enough electricity for hot water also. During the winter this will not be the case. This means when using a propan tankless water heater during the summer month you pay for propan while throwing away free electricity. Heating water with electricity means in the winter you have to buy electricy from the grid or use a generator (which is much less efficient than direct heating with propan).

I would use a mini split. It can also cool in the summer, no risk of combustion gases entering the tiny and easy to use. Even when a backup generator is used to generate the electricity a good one is not less efficient than direct heating with propane.