Is it possible to add the ability to enable productivity only for solar panels in the settings, without affecting the batteries?

Very unlikely.

Not because it cannot be done, it could be added. But if the goal is just increasing solar panel efficiency there's already this value https://lua-api.factorio.com/latest/classes/LuaSurface.html#solar_power_multiplier that could be changed at runtime.
So it would be a simple mod that with max 5 lines of code would do everything you're asking, instead of all this hacks I do in this mod to increase both panels+accumulators performance since there's no API for accumulators :) & would be a lot more UPS efficient.

In conclusion, I will not add that feature to this mod because it could be done differently in another mod which scope is smaller (limited to panels) and a lot better for game performance :)

Thanks for answer... I'll try to figure this out myself with chatgpt. (I've never make any mods, maybe it's time)

I mean code is pretty simple, but it's a nice first mod if you want to try. It should look like something like this: two files

-- data.lua
data:extend({
    {
        type = "technology",
        name = "solar-panel-productivity",
        icons = util.technology_icon_constant_productivity("__base__/graphics/technology/solar-energy.png"),
        localised_description = "Solar panel productivity",
        effects = {
            {
                type = "nothing",
                effect_description = "Increase solar productivity by +10%",
            },
        },
        prerequisites = { "solar-energy", "space-science-pack" },
        unit = {
            count_formula = "2500*L",
            ingredients = {
                { "automation-science-pack", 1 },
                { "logistic-science-pack", 1 },
                { "chemical-science-pack", 1 },
                { "production-science-pack", 1 },
                { "utility-science-pack", 1 },
                { "space-science-pack", 1 },
            },
            time = 60,
        },
    },
})

-- control.lua
script.on_init(function()
    storage.solar_power_multiplier = 1
end)

script.on_event(defines.events.on_surface_created, function(event)
    game.surfaces[event.surface_index].solar_power_multiplier = storage.solar_power_multiplier
end)

script.on_event(defines.events.on_research_finished, function(event)
    if event.research.name ~= "solar-panel-productivity" then
        return
    end
    storage.solar_power_multiplier = storage.solar_power_multiplier + 0.1

    for _, surface in pairs(game.surfaces) do
        surface.solar_power_multiplier = storage.solar_power_multiplier
    end
end)

beware it will not be compatible with Space Exploration (it has custom multipliers per-surface). But if you want to improve on that it will be a nice journey ;)

While I was struggling with chatgpt, it turns out you've already done everything for me, thank you very much. I feel bad asking you this, but could you tweak the code a little? So that this technology would add 20% bonus per research level and have a total of 20 levels of research (for a total of +400% bonus with all research). And so that the first 5 levels could be unlocked with red and green science packs, the next 5 with a blue science pack, and the remaining 10 with a space pack. And so that the cost of research starts at 1000 packs and increases by 1000 for each level. And one more question: will it be compatible with modded solar panels? For example, those added by the Krastorio mod?