I am trying to promulgate a neologism of near-time, like real but a little more relaxed. Like the version of time in the CAP theorem. Soon but not like, soon within a bounds. Soon.

Real-time needs to be taken within a context. Your realtime is probably way sloppy for like say laser that starts fusion reactions.

If I were baking a pizza, my watchdog could be set to 5 seconds and be ok (provided the thermal inertia of the oven wasn't ridiculous and my heat source wasn't the said laser).

Near-time. The future is in the near.