The one landing on Coruscant is supposed to be the Falcon. Whether it had that name at the time is anyone’s guess. There are three similar ships seen in AOTC when the refugee transport lands on Naboo.

The argument against the Falcon being new is we don’t see similar ships anywhere else in the OT. There can’t be many left still operating. Even the Rebellion doesn’t have a YT in it’s fleet of old beat up ships.
The wear and tear probably accumulates faster when you’re doing smuggling for the likes of Jabba.