Growing up in the US there are a lot of age-based milestones. You can drive at 16, vote at 18, and drink at 21. Once you’re in academia though, your actual age becomes much less relevant. Instead, academics are judged based on academic age, the time since you got your PhD.
Grants often have restrictions based on academic age. The European Research Council’s Starting Grant, for example, demands an academic age of 2-7. If you’re academically “older”, they expect more from you: you must instead apply for a Consolidator Grant, or an Advanced Grant.
More generally, when academics apply for jobs they are often weighed in terms of academic age. Compared to others, how long have you spent as a postdoc since your PhD? How many papers have you published since then, and how well cited were they? The longer you spend without finding a permanent position, the more likely employers are to wonder why, and the reasons they assume are rarely positive.
This creates some weird incentives. If you have a choice, it’s often better to graduate late than to graduate early. Employers don’t check how long you took to get your PhD, but they do pay attention to how many papers you published. If it’s an option, staying in school to finish one more project can actually be good for your career.
Biological age matters, but mostly for biological reasons: for example, if you plan to have children. Raising a family is harder if you have to move every few years, so those who find permanent positions by then have an easier time of it. That said, as academics have to take more temporary positions before settling down fewer people have this advantage.
Beyond that, biological age only matters again at the end of your career, especially if you work somewhere with a mandatory retirement age. Even then, retirement for academics doesn’t mean the same thing as for normal people: retired professors often have emeritus status, meaning that while technically retired they keep a role at the university, maintaining an office and often still doing some teaching or research.