How does it affect time travel if you start with the assumption that reality as we know it is a computer simulation?

In this case, time travel has nothing to do with physics, and everything to do with software simulations.

Time travel backward would require that the program saves all previous states (or at least checkpoints at fine enough granularity to make it useful enough for time traveling) and the ability to insert logic and data from the present into states of the program in the past. Seems feasible.

Time travel forward would consist of removing the time traveling person from the program, running the program forward until reaching the future destination, then reinserting the person.

Forward time travel is relatively cheap (because you’d be running the program forward anyhow), but backward time travel is expensive because you keep having to roll the universe back, slowing the forward progress of time. In fact, one person could do a denial of service attack on reality simply by continually traveling to the distant past. Then, every time you come back, you would have to immediately return to the past.