AFAIK original sin does teach that all men are fallen and require salvation. This doesn’t mean that human nature is all bad and it’s indeed not the same as total depravity. However it’s also not true that men are born holy.
The total in TULIP's "total depravity" is not a measure of sinfulness. It is not meant to imply that we are naturally as evil as possible in every context. The "total" is speaking in terms of the extent of depravity. That is to say, sin touches and influences every aspect of our existence. So that even in good works with the best of intentions humanly possible, there still exists an element of self exalting corruption.
I didn't say "born holy" but if you kindly turn to Genesis you can see how the first man and woman were CREATED in Original Holiness (and Solitude, Justice, Unity).
Original sin is a deprivation of these positive qualities. Mary, for example, preserved in holiness, not simply cleansed of it. Holiness is our natural state, and so baptism returns us to that preternatural holiness that Adam enjoyed when he walked with God in the Garden.
