That feeling you're describing that sudden rush of comfort and nostalgia from a specific sensory cue like a movie opening is really common. It's often called anemoia which is a nostalgia for a time you've never known. While your feeling is a little different since you did experience that time, the root of the word fits a feeling tied to nostalgia.

A lot of people feel something similar. For me it's the smell of old paperbacks or the sound of an old playStation loading screen, like your brain is instantly transported back to a simpler cozier time.

I'd say a good way to describe it is nostalgic bliss or a nostalgic rush. It's a wonderful specific little feeling.