You can't treat the same team as "different" teams because they're correlated and mess up your analyses. You'd need to do some type of longitudinal modelling line time series or mixed-effects models to account for the repeated instances over time.
Well... you need to use the quantile function or inverse CDF of the chi-square distribution for that and I don't think there are closed-form expressions for it because of the gamma functions involved.
Let's do this step by step. We'll start with something simple and build towards a full HLM. First, you have a few important-yet-ambiguous statements that need more precise definitions. What does "general characteristics of the attachment", "predicts the burnout risk" and "higher the attachment...
For models like yours the only way to approximate power is through a computer simulation. This can get you started:
https://www.tandfonline.com/doi/abs/10.1207/S15328007SEM0904_8
You're running into a combinatorial explosion problem, which is very typical of discrete mathematics.
But it shouldn't be too difficult to simplify the expression to something you can evaluate. If you're unfamiliar with how to simplify factorial ratios, here's something to get you started: