I did some testing to see what the C.Falcon changes actually do so here's the results.
Testing was done in training mode with 1 cpu set to control and 1-frame per ZL press
Changes are highlighted by: *
3.0.1:
1: When hitting King k. rool with Side-special, K.rool's jump comes out on frame-53 at 0%, and f-59 at 100% from the moment K.rool gets hit, with Side-special being initiated right next to K.rool.
2: Regardless of distance, the faf for K.rool after getting hit is always the same.
3: When K.rool stands in the starting position, C.falcon's Side-special connects when the tip of his left foot is on the outer-line of block -5.8, it does not connect on block -5.9.
4: C.falcon's faf after hitting with side-special is f-41 with K.rool at 0%, this is the same for long-distance, and with K.rool at 100%
5: C.falcon's Side-special hits on f-6 of foe-detection(f-16 of move initiation when next to opponent), same for long-distance
6: C.falcon's Side-special deals 18-frames of hitfreeze, and launches the opponent on f-19
7: C.falcon's Bair 15.6%-hitbox ko's Mario into the right-blastzone at 116% in Training mode-Battlefield's starting position(middle of right-platform) with no DI
8: C.falcon's Ftilt 9.6%-hitbox ko's Mario into the right-blastzone at 236% in Training mode-Battlefield's edge-of-the-right-platform with no DI
9: C.falcon's Ftilt 10.8%-hitbox ko's Mario into the right-blastzone at 215% in Training mode-Battlefield's edge-of-the-right-platform with no DI
3.1.0:
*1: When hitting King k. rool with Side-special, K.rool's jump comes out on frame-54 at 0%, and f-60 at 100% from the moment K.rool gets hit, with Side-special being initiated right next to K.rool.
2: Regardless of distance, the faf for K.rool after getting hit is always the same.
3: When K.rool stands in the starting position, C.falcon's Side-special connects when the tip of his left foot is on the outer-line of block -5.8, it does not connect on block -5.9.
4: C.falcon's faf after hitting with side-special is f-41 0%, this is the same for long-distance, and with K.rool at 100%
*5: C.falcon's Side-special hits on f-5 of foe-detection(f-15 of move initiation when next to opponent), same for long-distance
6: C.falcon's Side-special deals 18-frames of hitfreeze, and launches the opponent on f-19
*7: C.falcon's Bair 15.6%-hitbox ko's Mario into the right-blastzone at 109% in Training mode-Battlefield's starting position(middle of right-platform) with no DI
*8: C.falcon's Ftilt 9.6%-hitbox ko's Mario into the right-blastzone at 211% in Training mode-Battlefield's edge-of-the-right-platform with no DI
*9: C.falcon's Ftilt 10.8%-hitbox ko's Mario into the right-blastzone at 193% in Training mode-Battlefield's edge-of-the-right-platform with no DI
10: There is no difference in the speed at which C.falcon moves after initiating Side-special, nor is there a change in the timing of when he starts moving
There are also changes to Utilt, Fair, and Down-special, but I didn't bother testing those as Utilt's changes were already documented, and Fair and Down-special's changes are too much of a pain to test for.
So to put it simply:
Opponents can move 1-frame later after getting by C.falcon's Side-special
C.falcon's Side-special hits 1-frame earlier
C.falcon's Bair ko's roughly 7% earlier
C.falcon's Ftilt weak-hit ko's roughly 25% earlier
C.falcon's Ftilt strong-hit ko's roughly 22% earlier
(untested by me but included for the sake of being comprehensive)
C.falcon's Utilt hits and stops 3-frames earlier
C.falcon's Fair has a bigger hitbox
C.falcon's Down-special is longer active
The patch notes say that there is a "Reduced startup of when Captain Falcon starts moving forward", but this is incorrect; in this video
https://www.youtube.com/watch?v=1HCErTzAn6Y if you set the video to 1080p60 and press . and , to move forward 1-frame at the time from the 2:19 mark, you can see that he does not move earlier, and there is no difference in C.falcon's position during the move(make note of the fact that the old and new footage seem to start from different positions, I've attempted to show the difference here,
https://imgur.com/lnURp3h it seems that the new footage starts just slightly further to the right)
If this line refers to the post-foe-detection hit-startup, then I think it should be phrased like "Reduced startup of when Captain Falcon starts post-proximity-detection-hit by 1 frame"
The patch notes also say that there is "Increased hitstun" on Side-special, but this is incorrect; there is no difference to the freeze-frames, only to the launch-immobility. Admittedly hit-stun is a term used in this community to refer to launch-immobility, but as it is also used by nintendo to refer to freeze-frames, I think it would be better to use the term launch-immobility to avoid confusion.