I agree with the adjacent commenter: therapy would help with this.
As someone who has similar anxieties, I was pleasantly surprised in two ways when getting professional help:
Surprise one: the advice for confronting anxiety--specifically social anxiety around forming connections--was actionable and specific rather than woo-woo and "just be present/mindful/listen to your thoughts and they go away"-flavored.
Surprise two: therapists identified specific areas where I had broken or atrophied social skills and helped to build them. Just like crossing a street, most unprompted social interactions:
a) Have an expected script which, if followed, reduces the risk of severe negative consequences to near zero. If you didn't know the script you mentioned ("Wait until all traffic has stopped..."), then crossing a street would be dangerous indeed.
b) Have a higher likelihood of minor, non-lasting negative consequences: getting honked at by oblivious drivers, playing do-I-go-left-or-right chicken with oncoming pedestrians, bumping into people, and so on.
c) Have a lot of rules that are contextual (local traffic laws :: mores about what is acceptable in a park vs. in a pub). Some of those rules can be researched, but a lot of them are unspoken/gained through practice--and practice with others is most effective.
d) Are not practiced perfectly by most people. Those apprehensions you have? Those awkwardnesses and anxieties and hyper-awareness of the consequences of failure? Those are shared by tons of people! Even women in the dating scene--hell, especially women in the dating scene--are screwing up, recovering, bailing out, gathering themselves, and trying again constantly.
If you are worried about "missing some kind of sign and ... losing a job", that sounds a lot like either anxiety (therapy surprise one helps) or some missing/mis-functioning specific skills (therapy surprise two, and I cannot underline this enough, really helps here).
(Caveat: be aware that psych help, just like friends, car mechanics, or clothing stores, is variable in quality and highly preference-based; multiple selection passes may be needed before you find someone that you vibe well with).
I also really recommend Devon Price's writing on the subject. He has a few focuses that may be less relevant here (experiencing autism, being queer/trans), but also writes extensively on social/romantic interaction as a practiced, scripted phenomenon; I have found those essays to really help contextualize some of this stuff: https://devonprice.medium.com/
> I really do not get why people are against dating apps, when those are the best thing ever to avoid catastrophic consequences for initial approach.
I'm not against dating apps; I'm responding to the "unprompted social outreach is risky/a bad cost-benefit" claim.
In fact, you can get a lot more out of dating apps if you have practiced the skills required to be comfortable with ("comfortable with" is not the same as "good at") apropos in-person connection forming!
Also:
> nobody sane will blast you on social media
I agree. Raging about someone's social gaffe on social media is not sane/healthy behavior. Since jackasses raging online is nearly never as life-ruining as you might fear, framing it as "not sane and therefore not worth losing sleep over" is a good approach!
...and people on social media routinely rage about pedestrians, cyclists, slow drivers, etc. With pictures, license plates, death threats--the works. With dating, just like with crossing the street, it is not worth worrying about: be kind/do no harm, learn (potentially with help) the skills needed to progress, be willing to fail a lot while learning, and it will turn out well. I promise.
EDIT: Also, one last thing:
Avoid parts of the internet that use language like "daring to approach while ugly" and "on initial approach" when talking about dating. I've been there. I get how good it can feel to be validated by people with similar experiences, who explain that it isn't your fault/that thinking about dating as adversarial game theory is healthy. But those communities are toxic, self-hatred-reinforcing hostility factories. Seriously, go for a walk/watch TV/read a book instead.
If those are terms you came to use organically, consider avoiding them to avoid being associated with those places.