'Hot water heater' versus 'Water heater'

Correctness

Hot water heater

The phrase is definitely grammatically correct (it has no objective construction or structural issues). Whether it's appropriate usage or not is a different a question.

Analysis

I can think of two ways to parse the phrase:

Hot [water heater]: a water heater that is hot.

You know, because... it gets quite hot... as it heats the water.

[Hot water] heater: a water heater which further heats water that is already hot.

If you live in a desert, this might somewhat apply.¹ I do not know if there are special appliances for heating water that's already hot.

Short, nice answer

The phrasing is, indeed, somewhat redundant, unless there is a very special case that holds. A heater of object X does conventionally make object X hotter.

[1] Getting water when in a desert is a separate problem.

There is actually a relevant article discussing terminology (ie usage) at Wikipedia [emphasis mine]:

Domestically, water is traditionally heated in vessels known as water heaters, kettles, cauldrons, pots, or coppers. These metal vessels that heat a batch of water do not produce a continual supply of heated water at a preset temperature. Rarely, hot water occurs naturally, usually from natural hot springs. The temperature varies based on the consumption rate, becoming cooler as flow increases.

Appliances that provide a continual supply of hot water are called water heaters, hot water heaters, hot water tanks, boilers, heat exchangers, geysers, or calorifiers. These names depend on region, and whether they heat potable or non-potable water, are in domestic or industrial use, and their energy source.

So, the terms, whether appealing to logic or otherwise, are not used consistently. I suspect that this terminology may be different again here in the UK.

The appliance used to heat water is a "water heater" Some cars use electrical elements to warm the seats. There are "electric heaters". "Electric" is an adjective used to describe the type of heater My car uses hot water to warm the interior. This is a "hot water heater". "Hot water" is an adjective describing the type of heater.