I got my current 4 day gig just by being upfront with everyone I interviewed with that that's what I was looking for, and waiting until someone said yes.
Same, although I'd add it wasn't easy (in the UK.) I found most of the companies I spoke to the last time I was on the job market were open to me working 4 days a week. I made sure to raise my part time status at the earliest opportunity and added it to my CV to make sure I was only interviewing for positions where this could be accommodated.
However, when it eventually came to negotiating after successfully interviewing it was still difficult and I had at least a few companies - to my huge frustration - try to push me into a full time role or even tell me they weren't setup to handle my request yet but would be in future! With the role I eventually accepted I still had to work full-time during my probation period before I could reduce my hours due to limitations with their processes (apparently.)
To help answer the originl question, at my former employer - The Financial Times - a 4 day week was fairly common amongst folks with young children.
Same here. I just laid my 3 conditions (4 days week, 100% remote, X€ per month) right away in the introduction interview and made it clear that I wouldn't be interested to move forward if these were not met. Most companies I interviewed with were OK with this. The job market for SE (depending on experience) nowadays allows these types of requests with good compensation.