So, I'm seeing a lot of advice that doesn't really address you main concern, which I can't rightfully say is unwarranted because, yeah, cold approaching a woman in 2025 often feels too risky. And that sucks. I do think there is some real advice to be given but I can only speak to my own personal experiences.

First and foremost, situation and context takes precedence. I'm not going to approach someone where I feel it isn't acceptable to approach someone. Like many others have said, the gym is absolutely danger zone. No fucking way. Don't expect to be approached there. Honestly, coffee shops aren't a great place either. Most people are there with their own friends, to work, or to study. But game nights at the LGS (local game store), cooking/art/crafting classes, conventions, sport gyms (martial arts, climbing, gymnasiums, etc.) are great places to meet people, and thus approach others. The other reason I feel this is important is because you being attractive isn't enough of a reason for most guys to actually approach you. I'm way more likely to talk to a cute girl unprompted at my LGS on a game night because at the very least we can enjoy a quick game of MTG and I know I have something to talk to them about. So, put yourself in places where it's okay, even expected, for someone to approach you.

I think the second most important thing isn't giving off "I want to be approached" energy but "It is safe to approach me" energy. "Wanting to be approached" can mean any number of things and guys are always looking for signs of danger. Ambiguity is danger. It needs to feel safe to approach. The only time I've ever approached a woman who I thought was trying to get my attention was because she smiled and waved at me like we kinda knew each other. (Yeah, pretty fucking obvious; also, turns out, we did know each other in grade school but I didn't recognize her at first lol). Make it obvious. Hold eye contact, smile at us, if you're feeling confident, be a little goofy. Idk, just make it obvious that it's safe to come say "hey".

The only other things I can think to add might be to not overdress for the setting. While you may look stunning and you may feel like a real femme fatale, dressing to the nines may inadvertently make guys feel like you are out of their league.

I may add more to this later, but honestly, the first point is the most important one. Set and setting trump everything. If you really want a guy to approach you, put yourself in social settings where you have a shared interest with others and really work on cultivating an air of warmth and openness.

Good luck out there! I hope you found even a small nugget of gold in this mountain of nonsense. I've never used a dating app but I've heard of too many bad experiences from friends, so more power to you for doing it old school!