Countering an uncounterable spell, triggers, and state-based actions
You lose when you have to draw a card and can't, not when you have no cards left in your library

Your third bullet point is mostly correct.

All instances of Drowned Secret's triggered ability resolved, then Thought Collapse failed to counter Inescapable Blaze, but still did as many effects as it could, so you milled some cards. Then Inescapable Blaze resolved, and your opponent lost the next time State Based Actions were checked due to having 0 life.

In fact, even if you hadn't won the game at that point, you wouldn't have lost for having no cards in your library. A loss only occurs when a player attempts to draw a card and cannot because their library is empty. 


  104.3c If a player is required to draw more cards than are left in their library, they draw the remaining cards and then lose the game the next time a player would receive priority. (This is a state-based action. See rule 704.)


Emphasis mine.

Drowned Secrets simply 'puts' cards from a library into the graveyard. This isn't drawing cards, and if there are not enough cards in the library that the ability attempts to put into a graveyard, the ability simply does as many cards at it can. (It can do this to 0 cards) In this case, the first Drowned Secrets milled 1 card (as many as it could find), then the second Drowned Secrets milled 0 cards (because there were none remaining), then Thought Collapse tried to counter a spell (it failed) and milled 0 cards.



Also note that this sort of interaction is true for any kind of action that causes you to remove (but not draw) cards from your library. For instance, with Omen Machine in play, players will never lose because of rule 104.3c. They may lose through other means (damage, poison counters, etc) but they will not draw cards. Theoretically if an Omen Machine were on the field and players could not destroy it or meaningfully impact each other, play will continue until - and beyond - when players have no cards left in their libraries. (Though in that case, the game will probably end in a draw in a few turns, when the game's state hasn't changed and no player chooses to change the game's state.)