Kotaku managed to contact Sony, which responded as to why the trailer was private on the channel, citing "licensing issues."
It's likely that the title is indeed cancelled or in development limbo.
Update 9/29/2023 11:54 a.m. ET: A spokesperson for Sony said the KOTOR remake trailer was delisted over licensing issues. “As part of normal business, we delist assets with licensed music when the licenses expire,” they told Kotaku in an email. The only music in the trailer seems to be the main Star Wars theme which is owned by Disney.
It's likely that the title is indeed cancelled or in development limbo.