SI_INTERFACE_OPTIONS_HIDE_MOUNT_STAMINA_UPGRADE
These are string constants used for translations!
Behind SI_INTERFACE_OPTIONS_HIDE_MOUNT_STAMINA_UPGRADE you will find, via GetString(SI_INTERFACE_OPTIONS_HIDE_MOUNT_STAMINA_UPGRADE) the text of the translation.
Something like "Hide mount stamina enhancement".
-> Should help to find the relating settings, see below

Thanks to Feroc's Autoloot Toggle I got as far as this below, but obviously "autolootSetting" and "SETTING_TYPE_LOOT, LOOT_SETTING_AUTO_LOOT" needs to be replaced – Idk with what?

There is one settings category, or SettingSystemType in ZOs naming (SETTING_TYPE_LOOT) which holds these setting names/IDs (LOOT_SETTING_AUTO_LOOT) and you need to find that in the esoui source files at best:
https://github.com/esoui/esoui

If you do not now the setting name/ID you can e.g. search for the string constants like SI_INTERFACE_OPTIONS_HIDE_MOUNT_STAMINA_UPGRADE which you found already.

https://github.com/esoui/esoui/blob/593b7915d5c6b897a3077ee939b27d3e56b764cd/esoui/ingame/optionspanels/optionspanel_gameplay_shared.lua#L309

Many ingame settings categories and IDs are defined in the tables in the files in this folder:
/esoui/ingame/optionspanels/
https://github.com/esoui/esoui/tree/live/esoui/ingame/optionspanels

/optionspanel_gameplay_shared.lua

--Options_Gameplay_HideMountStaminaUpgrade
        [IN_WORLD_UI_SETTING_HIDE_MOUNT_STAMINA_UPGRADE] =
        {
            controlType = OPTIONS_CHECKBOX,
            system = SETTING_TYPE_IN_WORLD,
            panel = SETTING_PANEL_GAMEPLAY,
            settingId = IN_WORLD_UI_SETTING_HIDE_MOUNT_STAMINA_UPGRADE,
            text = SI_INTERFACE_OPTIONS_HIDE_MOUNT_STAMINA_UPGRADE,
            tooltipText = SI_INTERFACE_OPTIONS_HIDE_MOUNT_STAMINA_UPGRADE_TOOLTIP,
        },

        --Options_Gameplay_HideMountSpeedUpgrade
        [IN_WORLD_UI_SETTING_HIDE_MOUNT_SPEED_UPGRADE] =
        {
            controlType = OPTIONS_CHECKBOX,
            system = SETTING_TYPE_IN_WORLD,
            panel = SETTING_PANEL_GAMEPLAY,
            settingId = IN_WORLD_UI_SETTING_HIDE_MOUNT_SPEED_UPGRADE,
            text = SI_INTERFACE_OPTIONS_HIDE_MOUNT_SPEED_UPGRADE,
            tooltipText = SI_INTERFACE_OPTIONS_HIDE_MOUNT_SPEED_UPGRADE_TOOLTIP,
        },

        --Options_Gameplay_HideMountInventoryUpgrade
        [IN_WORLD_UI_SETTING_HIDE_MOUNT_INVENTORY_UPGRADE] =
        {
            controlType = OPTIONS_CHECKBOX,
            system = SETTING_TYPE_IN_WORLD,
            panel = SETTING_PANEL_GAMEPLAY,
            settingId = IN_WORLD_UI_SETTING_HIDE_MOUNT_INVENTORY_UPGRADE,
            text = SI_INTERFACE_OPTIONS_HIDE_MOUNT_INVENTORY_UPGRADE,
            tooltipText = SI_INTERFACE_OPTIONS_HIDE_MOUNT_INVENTORY_UPGRADE_TOOLTIP,
        },		

The settings name would be:
IN_WORLD_UI_SETTING_HIDE_MOUNT_STAMINA_UPGRADE
IN_WORLD_UI_SETTING_HIDE_MOUNT_SPEED_UPGRADE
IN_WORLD_UI_SETTING_HIDE_MOUNT_INVENTORY_UPGRADE

And now you still need the category for it.
https://github.com/esoui/esoui/blob/593b7915d5c6b897a3077ee939b27d3e56b764cd/esoui/ingame/optionspanels/optionspanel_gameplay_shared.lua#L289

Just scroll up a bit from the first found entries and you see the table's headline:
SETTING_TYPE_IN_WORLD

So category (SettingSystemType) is SETTING_TYPE_IN_WORLD
settingsNames are IN_WORLD_UI_SETTING_HIDE_MOUNT_STAMINA_UPGRADE, IN_WORLD_UI_SETTING_HIDE_MOUNT_SPEED_UPGRADE, IN_WORLD_UI_SETTING_HIDE_MOUNT_INVENTORY_UPGRADE

And these can be used with all the GetSetting, SetSetting, GetSettingBool, SetSettingBool etc. functions.

If it's even possible to do all three in one keystroke, can that just look like:

No, you need to use the setting functions always with params defined in the API description, which you can find here as txt file:
https://wiki.esoui.com/APIVersion#Live_API_version
-> "API TXT Documentation:"

Download the txt file and search for the GetSetting or SetSetting functions and you see their parameters needed:
Means your call to change the setting via a function, called from a keybind, would be something like:

"1" should be enabled, and "0" disabled

local isEnabledString = GetSetting(SETTING_TYPE_IN_WORLD, IN_WORLD_UI_SETTING_HIDE_MOUNT_STAMINA_UPGRADE) 
--returns "1" if enabled and "0" if disabled

local isEnabledBoolean = GetSettingBool(SETTING_TYPE_IN_WORLD, IN_WORLD_UI_SETTING_HIDE_MOUNT_STAMINA_UPGRADE) 
--returns true if enabled and false if disabled

SetSetting(SETTING_TYPE_IN_WORLD, IN_WORLD_UI_SETTING_HIDE_MOUNT_STAMINA_UPGRADE, "1")

Hope that helps to help yourself, if not just reply if you got any questions.
btw: here is how to setup keybindinds in an addon (if the AutoLoot addon is not describing it enough by it's code):
https://wiki.esoui.com/Keybindings