It's a pool, but it's just 1.6psi
You have a 48in deep pool. If the soil is compacted by age, a 4in pad on 4in gravel without rebar/mesh will suffice.
Add the mesh anyway to protect the pool in the unlikely event of cracks that develop in the slab.
Soil and Gravel are the secret
Gravel is 1/5..1/10 the price of concrete, it provides drainage to prevent erosion or frost heave directly under the slab and, more importantly, it provides an even support for the slab. Should the soil underneath move (water, frost etc..), the gravel will help keep the support even. This support is what will determine the life and load bearing capacity of the slab.
Therefore it's a much better investment than just thickening the slab.
The depth of your pool determines the pressure of the water on the concrete. A 48in column produces just over 1 psi of pressure on the concrete. This seems low, but it's in the ball park of normal home & office floors.
What about 3000psi concrete?
Now to your concrete: it will be rated in the range 3000 to 4000 psi. Is that overkill? And what about the slab thickness, where does that come into play?
With such high strength and such low loads, slabs still crack or snap, so what does matter then?
The compressive strength rating is not the number you need; it is more of a material property, and it matters for posts, foundation walls, and other vertical columns that hold up a structure.
A slab of at least 2in thick will already achieve the rated compressive strength. Increasing the thickness does not really matter in terms of its compressive strength.
It's the load capacity that matters
What does matters is the load capacity expressed as the maximum span of a slab under a certain load, e.g. a point load or a uniform load. And this is where thickness and rebar come into play.
The standard load for an office or home is a mere 0.7PSI (1 psi is 144psf) and at that load, a 4in slab can span 2.4m. (I'm not a mechanical/structural engineer, but this number can be obtained from load tables
This is of course not a perfect model of your use case: the pool exerts a higher load. However, to offset that, the generally even support provided by the soil & gravel is far more benign than a span support provided only at the edges of a slab.
What this calculation does tell you is that if parts of the soil start giving, or if tree roots put pressure under the slab, even a 4in slab will hold over voids as large as perhaps 1m or more.
The "flexural strength" is the property that matters, as can be seen in the set-up that tests it:
To answer you question: yes 8in is sufficient, and rebar will make it better, but all you need is 4in. What really matters is the support under the slab: well aged and compacted "fill" (preferably not clay or sand) plus 4in of gravel.
Suitable gravel is angular and to some degree compressible. For this application it doesn't have to compress hard. You will tamper it down with a plate vibrator so that it settles. Perform a walk test to ensure it's not loose and well integrated with the soil underneath. I would compact the soil only if it's loose or recently dug up. You can compact the full 4in of gravel in once go. No need to pour it in layers.
You can use "3/4in angular" (sufficient for walking traffic) or "highway dust" (better for roads and driveways). They are more properly named and characterized in the pictures below.
Enjoy and happy swimming.