How do I calculate the required sample size using Cohen’s d? How can I determine the effect size (d) if there is no previous study on the same variables? Is it acceptable to use a value of 0.8 (large effect size) for d, considering that other interventions—although not targeting the exact same variables—have demonstrated a large effect?
Given that you are unsure about the size of the true effect in the population, it would probably be wise to go with a small or medium size effect (rather than a large effect) so as not to underestimate the required sample size. Smaller effects require larger samples to be detectable. Otherwise, you may end up with an underpowered study if you run your sample size planning with an effect that is larger than the actual effect.
In terms of how to do it, you can use, for example, the free G*Power software:
https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower
IMO, Cohen's t-shirt effect size guidelines are dodgy even in psychological studies. Here are two relevant resources.
https://homepage.stat.uiowa.edu/~rlenth/Power/2badHabits.pdf
Article Avoid Cohen’s ‘Small’, ‘Medium’, and ‘Large’ for Power Analysis
Instead of expected effect size you could determine the smallest effect size of interest. I found the paper "Sample Size Justification" by Lakens (2022) very helpful: Article Sample Size Justification
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