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Do you rember which platform it was on?
My first search results in this:
https://en.wikipedia.org/wiki/Dreamfall:_The_Longest_Journey
According to the desciption this has two parallel worlds, a talking bird, an event called "the collapse" and is part of a series
Sanity is for the weakPutt-Putt Travels Through Time ticks a lot of the boxes, though your descriptions of it being "post-apocalyptics" make it sound like a game for an older audience.

I remember an adventure game my brothers played when I was a kid (late 1990's to early 2000's, but the game may have been older than that). I seem to recall it was a science fiction game that had some kind of time travel or dimension hopping plot, and I have a feeling it may have been a part of a series. The main character maybe time traveled with a companion, which I think may have been a talking dog or other animal. The setting was either dystopian or post-apocalyptic.
I don't remember much else aside from that.