All data is in the past. Even with a live feed, information does not pass instantaneously. All data is historical data. The amount of time passing between now and the collection is irrelevant, with the possible exception of the Old Evidence problem in Bayesian Epistemology. It is not relevant here.
It is important to make a couple of distinctions as well. Frequentist methods distinguish data and parameters. In this story, you are making a probability statement about data. That is a very Frequentist thing to do.
However, it appears that your problem is not well posed. You seem to be conditioning on it being a fair coin. This is a classical statistic problem if it is a fair coin. What produces the difficulty is that we know about the coin and not the system.
Your friend, Fast Eddy, thrice convicted of bunko-related crimes, has a reputation of being able to toss a coin either heads or tails one thousand times in a row. Your other friend, a four-year-old named Aloysius, loves to toss the coin in the air and catch it. Which friend is tossing the coin?
Let us change your question. A coin was tossed five hours ago on Pluto. It is currently five and a half light hours away. It is a historical event as it has clearly happened. If it is a fair coin, what is the probability that you will observe it landing on heads? You will see the coin toss in half an hour. Does it matter that it is a historical event?
A Frequentist conditioning on a parameter value is really a classical statistician.
Now let us consider the Bayesian statistician. If the person tossing the coin does not impact the answer, I will place infinite mass on .5 and zero mass elsewhere. My Bayesian predictive distribution will be 50-50. That is trivial, though, as the Bayesian statistician is now a classical statistician.
As to your final example, the 48 heads depends on whether the tosser observed the results. If they saw them, then the answer is either 0 or 1. If they tossed the coin over a 1000 meter tall bridge with fog to prevent any viewing, then there is the same probability statement issue as above.