Is this p-hacking? I'm currently looking into the gender pay gap using data from glass door (found via kaggle). The dataset has columns for gender, age, performance evaluations of employees, seniority, pay etc.
For context: I have learned a lot of Data Science/Machine learning/programming over the past few years, and am just doing a few of my own basic portfolio projects for practice, before applying for jobs.
I have done a fairly naive t-test, comparing average pay for men vs average pay for women. I am now looking to add in controls, comparing similar age groups, seniority, education level etc. I want to do more t-tests, as well as looking at a chi-square distribution and/or ANOVA.
As I do multiple tests A/B tests, I want to avoid p-hacking. I have a few hypotheses, for example I expect the pay gap to be greater for older age groups. But this is mostly exploring the data, I don't have a single hypothesis I am looking to prove for the entire study, nor do I have a political agenda.
I'm not sure it would really count as p-hacking as long as I choose which comparisons to make, and report everything. I would think it's only p-hacking if I selected which t-test results to report to help prove a hypothesis. Is this fair?
And another question (forget my data for a moment), with ANOVA, as it compares multiple groups at once to look for significance, is this not p-hacking?

It looks like p-hacking. Keep in mind that standard tests (e.g., t-test) are designed for testing a single hypothesis. In particular, if you get several p-values, such values are not independent of each other, especially if you look for effect heterogeneity across sub-groups. This usually leads to p-hacking (or data snooping).
Whenever you test multiple hypotheses, you should be careful, and take into account multiple hypotheses testing (e.g., Bonferroni correction) and False Discoveries. In alternative, rely on pre-analysis plans, where you specify ex-ante the (few) hypotheses  you want to test.
If you want more details on p-hacking, I suggest an easy reading (about 40 minutes, not technical at all) from the last economics nobel laureate Guido Imbens: Imbens (2021). If you are interested in treament effect heterogeneity, a data-driven alternative to pre-analysis plans and data snooping is proposed in Athey and Imbens (2016).
Regarding the ANOVA, I agree with @Dave's comment in opening a different question.
