[Sharpedge]

This is what I have done:

local function UpdatePvPStatsFrame()
    if not IsAddOnLoaded("Blizzard_PVPUI") then
        LoadAddOn("Blizzard_PVPUI")
    end

    C_Timer.After(2, function()  -- Delay for 2 seconds to ensure the AddOn is fully loaded and ready
        local conquestInfo = C_CurrencyInfo.GetCurrencyInfo(Constants.CurrencyConsts.CONQUEST_CURRENCY_ID)
        local weeklyProgress = C_WeeklyRewards.GetConquestWeeklyProgress()
        local honorInfo = C_CurrencyInfo.GetCurrencyInfo(HONOR_CURRENCY_ID)
        local lifetimeHonorableKills, _ = GetPVPLifetimeStats()
        local honorLevel = UnitHonorLevel("player")
        local currentConquestPoints = conquestInfo.quantity
        local conquestCap = weeklyProgress.maxProgress or 1350

        if conquestCap == 1250 then
            conquestCap = 1350
        end

        local rating = GetPersonalRatedInfo(SOLO_SHUFFLE_INDEX)
        local soloShuffleRating = rating or "N/A"

        pvpStatsFrame.honorableKillsValue:SetText(lifetimeHonorableKills)
        pvpStatsFrame.conquestValue:SetText(currentConquestPoints)
        pvpStatsFrame.conquestCapValue:SetText(currentConquestPoints .. " / " .. conquestCap)
        pvpStatsFrame.honorValue:SetText(honorInfo.quantity)
        pvpStatsFrame.honorLevelValue:SetText(honorLevel)
        pvpStatsFrame.soloShuffleRatingValue:SetText(soloShuffleRating)  
    end)
end

pvpStatsFrame:RegisterEvent("CURRENCY_DISPLAY_UPDATE")
pvpStatsFrame:RegisterEvent("PLAYER_ENTERING_WORLD")
pvpStatsFrame:RegisterEvent("WEEKLY_REWARDS_UPDATE")
pvpStatsFrame:SetScript("OnEvent", UpdatePvPStatsFrame)
pvpStatsFrame:SetScript("OnShow", UpdatePvPStatsFrame)

With that it does fix the issue of showing the correct rating. BUT, if you go Group Finder/Player vs Player the "Rated" and "PreMade Group" is still grayed out and cannot be clicked. The only way to resolve that is with a /reload, and everything works just fine.