What space applications use the 555 timer?
It's used for the same sort of stuff you'd use it for on the ground. As a timer, as an oscillator, for pulse generation, as a watchdog timer... you have many of the same needs aboard a spacecraft as in any other type of electronic system.
For most space missions, designers will specify uprated, space-qualified versions of standard parts. TI sells one such variant for the 555 timer, the SE555 which is classified as QML V (ie: suitable for space): https://www.ti.com/product/SE555-SP.
You certainly pay a premium for space-qualified components, though: TI lists the SE555 as $165 each in quantities of 100, which is quite a price delta when you consider a jellybean 555 goes for less than $0.10 in similar quantity.
This price difference is one of the reasons that low-cost space missions such as CubeSats and SmallSats use commercial or automotive components instead of space-qualified ones. The relability is lower, but the mission cost constraints prevail.
The other reason is usually part availability: as a rule of thumb, radiation tolerant space qualified components lag 10-20 years behind the current state of the art. Many of the missions enabled by small satellites are only possible due to the small size and high level of integration afforded by cutting-edge microelectronics. So, they accept the risk of using new commercial components as it would be very difficult to build a mission in that mission class limited solely to a selection of (largely dated) space-grade parts.