Thanks for this honest depiction of what it's like to be a man. Maybe I'll try the tinder thing.
As a feminist, I very much believe we need to have more emotional support for men. Men need to feel safe expressing their emotions, going to others, including other men for comfort, support, and community. I have heard of the weird staring contest thing, that's a total BX patriarchy move, where one man wants to be on top of the man pile as the patriarch. My ex-husband compared it t dogs sniffing each other's balls. I admit, I would not want to engage in any of that. Sounds very, immature.
I do know of at least two trans men, who lived as women then transitioned, and both told me the are treated better as men than they were before hand. The did say it was a lot harder on dating apps, one man was gay and eded up getting a husband after a few years. The other guy I know is bi and dates non-binary people as well as other trans men, so they have a different experience dating world. They both said in general they were given a lot more respect in everyday life and at work. I also know a number of trans women who talk about the difference after living as a man vs a woman. They often say men are expected to bottle up their emotions and aren't allowed to show it. However as women they aren't listened to and generally undermined at things, including at work. I think listening to trans people on this issue could provide insight, though as trans people they are often discriminated against a lot post-transition.
Personally, I have experienced first hand men with less experience and qualification getting promoted above me at work. I think if I was a man I would focus on my career and enjoy delving into that. There have been multiple times where receiving medical care had been greatly limited due to my gender, and there are clear examples of men in my family with the same diagnosis getting diagnosed, treated, being listened to by doctors at an earlier age. I also have a very serious condition (lipedema) that affects almost exclusively females that has been known about for 80 years and affects a lot women, but there are virtually no treatments and very little awareness for because it's easy to just victim blame women for our bodies than it is to find treatments.
The grass may always feel greener, and I think both greener, and even if we get a peak into the other side, we all have our biases. It's easy for me to want better health care, safety, and career prospects and feel lack of quality relationships is a minor thing, when I do have lots of dating options and lots of friends and community. So my own bias from my history may impede my response.