What is the consensus on reaching out to people from a company or hiring manager from a job you just applied to?

What is the consensus on reaching out to people from a company or hiring manager from a job you just applied to?

So I’m currently employed, but I am in need of a higher salary after a breakup left me paying 100% of expenses on my own. I have been getting rejected without a screening for jobs I am perfectly qualified for because the volume of applicants is so high. I don’t really have a network to reach out to. My previous colleagues are all still at the company that laid me off, so I don’t have any internal connections at the companies I’m looking at to receive a referral.

I have been advised by friends to find people at those companies and message them to introduce myself after applying. My recruiter friend (she recruits doctors so she’s not able to help with the roles I’m looking for) gave me a script for how to introduce myself. I did that once and was blocked and then received the rejection email for that job from it. I’ve read threads online where hiring managers and recruiters say they will ignore your message or block you if you contact them and that they want you to just cold apply like everyone else. But it’s the advice that is constantly getting floated around that cold applying isn’t enough and you need to follow up with a personal message. It leaves me feeling kinda defeated and confused on how to actually get noticed getting those mixed responses.

If you’re a hiring manager or recruiter, is this a myth that it’s a good idea to follow up with a message after an application?