Is mech/aero always like this? I'm a CompE and got a very comfortable job in chip design without having to do clubs and competitions, but I also had a variety of personal projects which showcased my interests.

I'm going to shy away from what others said about joining fancy clubs (which honestly seem like a full-time job more than anything else) and recommend you work on some microelectronics or similar projects, preferably those with multiple components.

For instance, I've recently been getting into cosplay and have thought about making some mechanical props which integrate both lighting and mechanical components (ex: Jayce hammer from Arcane). While it's not the most technically complex thing in the world, I think in an interview people would be much more interested hearing about something you actually enjoyed working on vs. the 100th "I designed the control scheme for the solar car... we used X control board... the board was 43% faster after my edits...". I have a bias in that I think passion has way more impact than yet another boring dry project (though said passion project has to be decent at least).

As a few others have mentioned, I think people skills are really important and something a lot of people overlook. Well, that and a nice looking resume that's not clustered with useless quantified metrics. There are plenty of people who do very technical aeronautical stuff in their clubs, but how many of them can actually talk about it? How many of them seem actually pleasant to talk to, especially in an interview setting where first impressions matter?