I think you are very much in the baby bubble still. You are clearly clever and your brain will need more stimulation than potty training at some point.
I was a SAHM when my eldest was a toddler and by the time he hit preschool I needed to work for my own sanity. Like you I adored being there for his firsts but it was not good for my mental health to have nothing more in my life. I did judge my mum friends who went straight back to work when baby hit 1 if they didn't financially need to - their careers are flying now and mine is not - that doesn't matter hugely to me although it is a big sacrifice.
I now have 3 children who are al at school and I work freelance part time and am there for them as much as possible, while my brain and self esteem and family finances benefit from my working.
I was a 'SAHM' when each of them were little though, didn't work at all for long periods.
I think don't completely identify as a SAHM (why I put it in quotation marks previously) because it's something you can do and be for periods when it works for you and your family, and you can dip in and out of work if you are clever about it.
Once you have more kids and they are older I'd bet money on you feeling differently about it.
Enjoy the baby days!