This is an improvement over the old TAS and beats it by 2.12 seconds, if you want an explanation on how all of the glitches work they have already been explained in the submission for the old TAS.
In Level 4 an intentional slowdown is used to avoid losing the mushroom, this loses 38 frames (1.46s) but keeping the powerup will be very useful in the next level.
Going into Level 5 with a mushroom allows the TAS to speedglitch off the ceiling above the second pipe in the level, which is way faster than the previous method where a mushroom was grabbed. This ends up saving 70 frames (2.69s) and puts us 32 frames ahead (1.23s).
In Level 7 another intentional slowdown is used to avoid taking damage, from the piranha plant by stopping at the second pipe and then doing speedglitch off the ceiling above. This loses 14 frames compared to the previous TAS but will save time in Level 8 (0.54s).
The fireflower in Level 8 allows for a way faster start, unfortunately there is no way to get perfect speedglitch off the first block in the level and keep it so the TAS has to slow down and do it on the block after that instead. Starting with fireflower in Level 8 ended up saving 35 frames (1.35s). If you combine Level 7 and 8 that is 22 frames of timesave (0.85s) which puts us 54 frames ahead (2.08s).
Level 10 has also been improved by 1 frame by doing speedglitch faster putting us 2.12 seconds ahead of the previous TAS.
Shoutouts to upelly for bringing up the idea of slowing down in Level 7 to save more time in Level 8 (which also lead to the slowdown route in Level 4).