"Hey James, I see you are working at Microsoft in Azure Compute and I am interested in breaking into that too. Would it be possible to go for coffee or catch up on Zoom?"
You may have to remind them how they know you if it has been a while :).
Keep it short. Unless you know they like a long email!
Why would anyone respond to that? I haven't talked to you in 15 years and barely knew you. Looks like you are working at Google, I want a job there too. Lets catch up on zoom.
If any past coworker I liked wanted to get lunch I'm up for it. For me it's not yet exceeded 8 years back so I guess I can't demonstrate that yet :). I also get a referral bonus so I do want to refer people!
We live in a world full of uncertainty. When someone you know is in a current need, helping that person is one way to hedge against the uncertainty of the future. Who knows, one day you may need such help too...
That's why this advice is common. It's important to be clear about the reasons for reaching out.
I've made a habit of just cold calling my friends because I thought of them. I'll usually end up talking to them for an hour or more, even if I had nothing I specifically wanted to talk to them about. Just "hey I was just thinking about you and thought it would be good to catch up, how've you been?" Something like that.