wondering if theres a name for this

My dad used to fix up bikes when i was little and i had a custom one just for me.
a while after we stopped talking, i wanted to get myself a new bike and tried finding something like what my dad would do for me but no one understood!

It was basically a fixie (pedals would move with the back wheel) but he slapped some breaks on there also. Is there a name for this?

I know it kind of goes against the principle of a fixie, but in truth i feel like i truly had the best of both worlds; energy saving + connectivity with my bike
while also being able to safely break if needed.

I know some snobbish bike people might hate the concept, but this its just what i found works for me.

So is this a thing or will i have to learn to fix up bikes myself?