[Baertram]

It should be enough to create your IO_BLUR_FRAGMENT fragment and add it to HUD_SCENE once

HUD_SCENE:AddFragment(IO_BLUR_FRAGMENT)

Attention: This will make it show as soon as you close a menu, or move, as the HUD_SCENE will be shown then.
To prevent this you'd have to either remove the fragment from the HUD_SCENE if it should not show, or add some condition at the
OnStateChange callback (see one of my last posts about it): As the FRAGMENT_STATE_SHOWING occurs -> check the actual stamina and if it's above the threshold hide the fragment again!
Shoudl be possible via IO_BLUR_FRAGMENT:Hide()

For your stamina OnPowerUpdate checks:
Scene fragments should use the base class ZO_HideableSceneFragmentMixin, and that class provides a function
:SetHiddenForReason()

ZO_HideableSceneFragmentMixin:SetHiddenForReason(reason, hidden, customShowDuration, customHideDuration)

So you could use that function to show/hide the fragment based on the stamina percentage:

IO_BLUR_FRAGMENT:SetHiddenForReason("StaminaThresholdChecks_FreeTextAfaik", (staminaPercent > thresholdValue and true) or false, 0, 0)

Edit:
Example code

local function hideTLCIfNotStaminaThresholdMet()
 return currentPlayerStamina > thresHoldStamina --return true = hide, if stamina is high enough
end
 
local fragment = ZO_HUDFadeSceneFragment:New(TestTLC, nil, 0)
    local function OnTestTLCFragmentStateChange(oldState, newState)
        if newState == SCENE_FRAGMENT_SHOWING then
d("[TestTLC]Fragment showing")
            fragment:SetHiddenForReason("ShouldntShow", hideTLCIfNotStaminaThresholdMet(), 0, 0)
        --elseif newState == SCENE_FRAGMENT_HIDDEN then
        end
    end
    fragment:RegisterCallback("StateChange", OnTestTLCFragmentStateChange)
    --Hide in menus/Show at fighting UI
    HUD_SCENE:AddFragment(fragment)