The Tome of Battle errata never gets as far as searing blade—it starts to correct firesnake (a maneuver in desperate need of errata), but instead of indicating what text you are supposed to add to the maneuver, the file’s contents is overwritten by the errata for Complete Mage. Yes, really. It’s still on Wizards’ web site like that, and it’s still really embarrassing. So the lack of errata here is not particularly meaningful.
Ultimately, boosts are defined as swift actions:
A boost always requires a swift action, usually allowing you to initiate it before unleashing a standard action or a full attack.
(Tome of Battle pg. 42)
And searing blade in particular makes absolutely no sense as a standard action, since it provides a bonus on attacks until the end of your turn. If you used a standard action to turn it on, that would make it apply to precisely zero attacks, since with your standard action down you aren’t going to be making any attacks.¹
So yeah, it should be a swift action. Tome of Battle is a fantastically well designed book, but it is not a terribly well edited book.
- Not strictly true, a factotum could and there might be some shenanigans you could do to get someone to provoke you in the middle of your turn, but it’d be very hard and very limited.