It really depends I think on the professional, your diagnosis/presentation, previous history, bed capacity. Sectioning is generally a last resort and if there is no other way for you to safely have treatment at home. An attempt doesn't necessarily mean that you'd meet the criteria for the mental health act and even if you do, they may let you off due to no room on psych wards
S136 is pretty common section, that's where police can take you to place of safety (e.g A&E) but it only lasts 24hrs and most people are just sent home after. I think it's pretty difficult to get sectioned for hospital stay (S2 or S3) in UK as there just isn't enough psych beds. So most of the time after attempts people are just sent home to either no support or crisis team. Some people are sectioned after first attempt but I think it's have to be very medically serious and also if maybe you tried to run away from hospital or harm yourself whilst being treated, anything that meant you didn't have capacity. But even then not guaranteed as heard of people who have had attempts landing them in ICU and saying they have further plans to then just be discharged. Or people who are discharged and immediately try again and succeed that time.
I think you most likely to be sectioned if you clearly can't demonstrate capacity. For example, severe psychosis where you're having delusions and hallucinations. Anything else they're just like 'well you have capacity to understand and kill yourself'.
I was sectioned once after an attempt for a month (had literally barely started attempt and was stopped by police, yet wasn't sectioned when id ended up in resus) but I'd had several previous attempts (some pathetic attempts before I found here , chickened out or was found) and I've lost count of how many times I'd landed in hospital for self-harm prior to this. It was only because my mental health team had already had a meeting considering mental health act assessment and repeatedly pushed for it as they were sick of me.