It's a hydrogen/oxygen engine (https://en.wikipedia.org/wiki/BE-3), the exhaust is basically water or maybe hydrogen peroxide.

https://space.stackexchange.com/questions/16821/what-is-the-...

The Space Shuttle burned hydrogen and produced water, none of which are really easily visible to the human eye. If you look closely at a launch you might be a able to catch a glimpse of the heat shimmer from the main engine.

Worth noting that you're talking about what's going on after the SRBs finish firing. The solids produce a lot of visible exhaust.

The space shuttle main engines did fire at liftoff while the SRBs were firing. They may be a bit hard to see at launch but the exhaust mach diamonds are clearly visible e.g. in [0]. They were much more clearly visible in the 7-ish seconds before liftoff, after the SSMEs had been ignited but before the SRBs go off.

[0] https://upload.wikimedia.org/wikipedia/commons/d/d6/STS120La...

Sorry, I didn't mean to imply that the SSMEs were not firing at liftoff. Since they fire for a few seconds before the SRBs get lit, I suspect most people know what's going on with them.

Yeah, ammonium perchlorate doesn't burn as cleanly as liquid hydrogen does.