[DahkCeles]

Here is a complete addon.

Press M to open and close the map.

While the map is open, press left-shift and left-control to go up and down the quests. It starts at the top, so you will need to use left-control to navigate to the first quest. Press tab to repeat the name and number of the quest.

While at a quest, press left-alt to hear the full description slowly, or right-alt to hear the objectives more quickly.

To be clear, you are not actually changing the game's selected quest when you use this code. It is simply navigating its own table. A more advanced version of this would probably integrate with the quest log to actually choose quests.

local quests = {}
local questSelected = 1
 
local function speakText(spokenMessage, speed)
    C_VoiceChat.StopSpeakingText()
    C_VoiceChat.SpeakText(1, spokenMessage, Enum.VoiceTtsDestination.QueuedLocalPlayback, speed or 5, 100)
end
 
local function readCurrentTitle()
    if quests[questSelected]["isHeader"] then
        speakText(questSelected .. " is a header: " .. quests[questSelected]["title"])
    else
        speakText(questSelected .. " is " .. quests[questSelected]["title"])
    end
end
 
local function readCurrentDescription()
    if quests[questSelected]["isHeader"] then
        speakText("Sorry, that is a header.")
    else
        speakText(quests[questSelected]["title"] .. ": " .. quests[questSelected]["description"], 2)
    end
end
 
local function readCurrentObjectives()
    if quests[questSelected]["isHeader"] then
        speakText("Sorry, that is a header.")
    else
        speakText(quests[questSelected]["title"] .. ": " .. quests[questSelected]["objectives"], 4)
    end
end
 
local function next()
    if questSelected < #quests then
        questSelected = questSelected + 1
    else
        questSelected = 1
    end
    readCurrentTitle()
end
 
local function prev()
    if questSelected > 1 then
        questSelected = questSelected - 1
    else
        questSelected = #quests
    end
    readCurrentTitle()
end
 
local function goto(i)
    if not tonumber(i) then
        i = 1
    elseif i < 1 then
        i = 1
    elseif i > #quests then
        i = #quests
    end
    questSelected = i
    readCurrentTitle()
end
 
local frame = CreateFrame("Frame", nil, QuestMapFrame)
 
frame:RegisterEvent("QUEST_LOG_UPDATE")
frame:SetScript("OnEvent", function(__, event)
    if event == "QUEST_LOG_UPDATE" and not QuestMapFrame.ignoreQuestLogUpdate and QuestMapFrame:IsShown() then
        wipe(quests)
        for i=1, C_QuestLog.GetNumQuestLogEntries() do
            quests[i] = C_QuestLog.GetInfo(i)
            if quests[i]["questID"] > 0 then
                quests[i]["description"], quests[i]["objectives"] = GetQuestLogQuestText(i)
            end
        end
        if questSelected > #quests then
            questSelected = 1
        end
        readCurrentTitle()
    end
end)
 
frame:EnableKeyboard(true)
frame:SetPropagateKeyboardInput(true)
frame:SetScript("OnKeyDown", function(__, key)
    if key == "LSHIFT" then
        prev()
    elseif key == "LCTRL" then
        next()
    elseif key == "LALT" then
        readCurrentDescription()
    elseif key == "RALT" then
        readCurrentObjectives()
    elseif key == "TAB" then
        readCurrentTitle()
    end
end)

Edit: I wrote mine before you edited your post.