Taking your second point/question first, vis-a-vis post hoc power which, of course, retrospectively uses the end of study observed data only to re-estimate power, there are numerous papers and online discussions on the topic, with this one from Andrew Gelman from 2019:
a discussion in this forum just prior to the above:
“Observed Power” and other “Power” Issues
and a 2021 paper by Andrew Althouse, who is a participant in this forum and initiated the thread above:
Post Hoc Power: Not Empowering, Just Misleading
On your first point, there are a plethora of considerations vis-a-vis interim futility monitoring and possibly associated sample size re-estimations, which at the top of the flow chart would be, are you using a frequentist or Bayesian approach. In conjunction with that are considerations for the type of endpoint (e.g. binary, continuous, time to event), along with other relevant study specific considerations that will impact the modality to be used to support interim decision making.
I would point you to a very recent (June 2025) open access paper/tutorial as a starting point, if you want to go down the rabbit hole a bit:
Futility Monitoring in Clinical Trials
There are numerous references at the end that are also of value, along with entire books on the subject, as there is no “one size fits all” approach to interim monitoring and decision making.
One general distinction that I would make is to keep in mind that many (most?) clinical trials begin with overly optimistic estimates of the treatment effect size. In the absence of formalized mid-study monitoring and adjustments, that will frequently lead to underpowered and inconclusive studies, which was the original basis of this thread.
Thus, in the context of formalized interim monitoring, the key question may not be “what is the probability that we will observe the original a priori hypothesized effect size?”, but rather “what is the probability of a non-null result that is still clinically relevant?”