That SmartThings routine action “dim/brighten gradually” is indeed a cloud based action that updates the state of the lights every 60 seconds or so. While it would work for every light even if they don’t have native transitions, it’s never going to be as smooth as invoking the native transition if available.
Now, for some lights using Zigbee there are custom drivers and, also for Matter, workarounds with the rules editor to call the native transitions. The problem is Lutron integration is not even local, is cloud based, so it probably doesn’t even support transitions, you can try the workaround checking if the setLevel attribute “rate” does something. I believe it won’t. In that case you could ask Lutron support to implement it or just ask how to use transitions from SmartThings.
Wall remotes use other proprietary protocols to communicate with the lights and achieve the desired effect and Home Assistant is also able to trigger native Lutron transitions but their integration is local and not cloud based so the feature set may be different.