> Early toilets on both the space shuttle and the International Space Station (ISS) used this vacuum system

For liquid waste. This was not exactly the case for solid waste. Effectively it was just a tank. It had something like a "net" in it, this was connected to a shaft, through a gear, to another shaft at the front of the seat. The commander would, every 7 days or so, "actuate the mechanism" to rotate the net and to gather all the waste and compact it into one side of the toilet.

Many commanders said this was the most stressful part of the mission as the mechanism was somewhat delicate and could easily break. In that case you had to don a glove and manually do the work the net was otherwise doing.

If that completely failed, yes, the shuttle had backup "Apollo bags" stored in the middeck lockers.