Calculating rechargeable battery charging rate curve

There are multiple techniques with various tradeoffs between them. If you search the literature for "battery fuel gauge" you should come up with a number of techniques.

Note that you can actually estimate SOC from voltage, provided the load is zero and the battery has been allowed to rest in this state for a while (hours). This relationship is not linear though, so you need to characterize the particular battery you're using and use some sort of a lookup table. Your voltage measurements also need fairly high precision and accuracy.

A more reliable method is coulomb counting, during both the charge and discharge cycles. This will provide a very accurate assessment of the amount of stored energy, and you only need to subtract out any self-discharge (which should be very small). However, measuring the current is a bit more costly, in terms of size, power loss, and $. And due to the self-discharge rate being variable and unknown, this technique needs periodic calibration or it will start to drift off from the true reading. This is typically done by resetting the high and low points after a full charge or full discharge respectively.

You can also combine these techniques (and possibly others) for even more accuracy and to mitigate drift effects.

This is how one manufacturer of battery fuel gauge ICs implements it: https://www.maximintegrated.com/en/design/partners-and-technology/design-technology/modelgauge-battery-fuel-gauge-technology.html

Irradiance is the solar power available per unit area (eg. W/m²) at any given instant. Insolation is the total energy (power * time) received over a specified period. For charging a battery the insolation is generally more important, but peak irradiance may also be a factor.

In your case the regulator limits useful irradiance to what it needs to produce 12V at 1A. Any excess power will simply end up wasted or not used, so the maximum power collected flattens off at a bit over 12W. How this relates to irradiance depends on how much your panels can actually collect. If they can't produce more than 12W anyway then the normal formulas apply. If they can then the irradiance required to produce 12W becomes the effective upper limit. This obviously also limits the useful insolation, but by how much? The answer isn't simple because it depends on the shape of the irradiance curve (useful insolation is the area under the irradiance curve after its top has been chopped off).

You may think that having a panel which can produce a lot more than you can use is a waste, however it may still have advantages. One is that the power collected is more constant for longer, so the battery is more likely to get fully charged even on cloudy days. Another is that if a load is also connected then excess power can be diverted to it, leaving more available to charge the battery. Also the battery can be charged at a more gentle rate than in a setup which must charge rapidly to collect as much energy as possible during the short time of peak irradiance.