You could get red coins in SM64 at any point in time. SMS had events that would only happen when you start a particular shine sprite.

In Mario 64, the worlds were open and there were more of them. Most of the stars were accessible to you regardless of which "mission" you selected when entering the world. This is because the mission you select usually doesn't actually affect the setup of the level - with a few exceptions like the Koopa the Quick missions.

In Sunshine, the opposite is true - more often than not, the mission you select can have drastic effects on the level, rendering certain Shines (Stars) unavailable, though there are exceptions. Some missions might start you off with the entire level covered in gunk, say, or with a boss roaming the world. This makes each mission more unique and memorable, but detracts a bit from the freedom that Mario 64 gave you. However, the worlds are still very much open for you to explore at your leisure - you just won't be stumbling across many unexpected stars.

I said Sunshine started the trend towards a more linear design structure in 3D Mario games, not for the series as a whole. Super Mario 64 is the most open ended game in the series in terms of how you can complete most levels at any given time. That's the design Super Mario Odyssey is based off of.

The problem is that you're literally saying Super Mario Sunshine started trends that it didn't. Acting like the 3D games were not at all impacted by the games that came before is absolutely ridiculous. Nintendo didn't just straight up ignore their 2D design models in advancing towards the 3D realm. The only reason I got any disagrees is because it's not cool to say something that may be seen as remotely negative towards Nintendo's design decisions, since "linear" has become such a dirty word in the past 10 years. God forbid someone actually think something through before spouting their small picture idea as fact.

And you seem to be acting as if I'm talking about the entire Mario series as a whole rather than just the 3D entrees.

The 3D Mario games are handled and treated entirely differently compared to the 2D entrees, just as the 3D Zelda & Metroid games are different from the 2D entrees in those series.

There may be some influences here and there, but each dimensional set of games are treated as their own thing in each respective series.