This feels like such a simple rule but I don't remember where the rulebook specifies where check-independant (not "on x checks") and non-reaction (not "when you x") cards can be played or not played, for example, powers that display, heal, or examine.
I know that during encounters, check-independant cards generally can't be played
I have been running the game with the idea that check-independant cards can't be played after the end of turn phase has been started until the hour has been drawn and resolved, because that feels like it's "in-between turns", where only boardgame admin should be occurring (otherwise you could do weird stuff like interrupt halfway through a reset with a heal that shuffles the deck and changes what cards are drawn). So, for example, if I draw an armor or a healing potion during reset, I can't play it until the next player has drawn the hour and all the Start of Turn effects have resolved (like ones that cause encounters)
But tonight we played CotC 4A with 6 x Collapses in the hourglass 😬, and it seemed pretty cruel to rule "no instantly playing drawn armour" if I didn't have a definitive explanation of why a player can't play their armour card they just drew for a pertinent event that was about to occur
You are essentially correct in your interpretation of the time span during which you can't play check-independent and non-reaction cards. (Well-described!)
The Core Rulebook added the following to its definition of Display: "Displaying a card and immediately activating a power on it counts as playing it once, not twice." So, you can display a card and immediately activate one of its powers any time it's appropriate. It doesn't have to be displayed before you want to use it. Thus, if you took damage, you may display and use your armor to reduce that damage.
Cards can be played:
1. Without limitation in between steps of a turn as long as it directly affects the situation
2. During an encounter, check, or when suffering damage: whenever it directly affects the situation and no more than one card of each type is played (not counting those played “freely”). Whipstitch raises a salient point of you being allowed to display and immediately use an armor card due to that only counting as playing it once.
3. During a step of a turn but outside of an encounter/check/damage only when the card has explicit timing allowing you to play it at that time.
Cards can never be played:
1. Between turns
2. Between steps of an encounter
Remember that cards can only ever be played if they affect the situation. So even if you’re between steps of a turn you can’t play a card that wouldn’t do anything. For example, no playing Cure on yourself when you have no cards in your discards and no scourges that can be removed in place of healing.