What you’re trying to do, albeit incorrectly (which is understandable) is a regression discontinuity design or regression kink design to determine the change. First I’ll answer your question then go into those designs.

For regression, you would need to do a power analysis (https://www.statskingdom.com/sample_size_regression.html) you can google how to do it manually if you want).

For things like a t-tests to comparative analysis 96 is generally large enough for any strata or group (simple random samples effectively have one stratum). However, if you want to compare groups/conduct subgroup analyses you need to ensure that all groups have adequate sample size. E.g. a class I TA’d drew a 127 person sample and only 7 were female student veterans thus it wasn’t possible to compare things like disability rating award rates between male and female student veterans for a survey. This problem is addressed by strategies sampling where you stratify your sample by the levels/subgroups of the relevant variables, ensuring that all subgroups have an adequate sample. So if I was concerned about veteran status, student status, gender, race, and disability status that would mean I would have at least 10 sub groups (depending on how you set up the variables). As you can see, this can present an issue if I simply base my sample on overall sample size and margin of error calculations. N=50 is enough to do a regression, but if I split that evenly between groups, i wouldn’t be able to do t-testing or much anything else. In your case, if you wanted to do that comparison, you’d want to double whatever you decide is an adequate sample size. Problem with your approach is that it’s an improper implementation of a proper method and that method probably wouldn’t be useful for this scenario anyway because there is no specific treatment, so discretizing the age variable likely wouldn’t be useful. It would be useful if there was some intervention at 1 yr because it is assumed that the responses right above and below that 1-yr mark would be similar and continuous absent the intervention.

However, As your design doesn’t include an intervention, it’s unlikely that discontinuity applies and, if anything kink design would apply (discontinuity is a vertical jump in the plot, such as glucose before and after insulin in 15min intervals. Kink is a stark change in slope, an inflection point. The rise in opioid OD deaths after the crackdown on pills would be an example). There’s another possible method called interrupted time series but that’s way beyond anything you’ll know how to do for a while anyway and I don’t understand it well enough to say if it could be used.

With that being said, I would simply plot the data to see what your graph looks like. If the data plot is linear, including a cutoff value wouldn’t be useful. And it is possible that there’s even a nonlinear relationship for some reason. In reality, unless that plot shows a jump or stark change in the slope (think a kink in a pipe), a normal regression would suffice given that there’s no reason to expect a stark change of any kind because it is continuous and there’s no intervention to cause it. So plot your data and do a simple regression first. If the results don’t make sense, make a post with a screenshot of the plot and also the output data.