Recruiters told you those roles don't exist because recruiters are compensated on a percentage of your salary. Lower salary, lower fee, but it takes the same amount of work to fill the role. So why should they bother with part-time when there are loads of full-time roles to chase?

However, remote part-time does exist! If you're a frontend developer looking to fill a few extra hours on contract feel free to reach out - my email is in my profile.