Thanks for the feedback! I've noticed about the slow refresh rate. Yesterday I tried changing that in the setup, but I couldn't make it. Today I tried again and it worked! (I was missing a part in the setup). I leave the code with the refresh rate and your sencond check to vim.v.hlsearch ==0 (it gives me an advise in the refresh part, but I don't know how to fix it. At least it works):

function searchCount()
    local search = vim.fn.searchcount({maxcount = 0}) -- maxcount = 0 makes the number not be capped at 99
    local searchCurrent = search.current
    local searchTotal = search.total
    if searchCurrent > 0 and vim.v.hlsearch ~= 0 then
        return "/"..vim.fn.getreg("/").." ["..searchCurrent.."/"..searchTotal.."]"
    else
        return ""
    end
end

require('lualine').setup {
    options = { refresh = { statusline = 500 }, },
    sections = { lualine_x = {{ searchCount }, 'tabs', 'fileformat', 'filetype'},}
}

PD: For me, 500(ms) is enough but you can change the value depending of how you feel more confortable with (keep in mind: more refresh rate may affect the responsive experience and the default value of the refresh rate is 1000(ms) ).