During my job search, I'd do my best to get the decision-maker on a call. This could be a co-founder or eng manager or an outsourced recruiter. If there was good rapport on the screener, and I felt like I could be vulnerable to them, I'd mention it like "hey by the way, I don't want to waste your time with this... I won't be able to pass a background check."
At that point they'd often be surprised and I'd just be honest with them with what happened. I only remember one time it didn't work out.
I never would bother with sending a resume to HR or an internal recruiter. They see 100s of resumes and if I were to put "hey I'm a felon so don't waste your time unless you're chill" on it, I'd get put into the pile I wouldn't want to be in.
Having an opportunity to build a relationship prior to full-disclosure always proved to go astonishingly well.
My crimes didn't change anyone's immediate future or harm any children; it was white-collar. I'm also fairly articulate. I imagine it would have been more difficult if the nature of my offenses were different, or if I wasn't as (seemingly) intelligible.