Backpacking is the essence of travelling you describe. Just buy a return ticket, some guidebook (not necessary but usually more help than harm), maybe a local phrasebook. Ideally avoid most touristic places or zoom through them quickly.

Living in the moment, many unplanned unique experiences every single day, 2 week vacation feels like a month or two passed by.

I did that in India&Nepal twice, each time 3 months, and I literally forgot about reality back home, it felt like 5 lives before, memory of a distant dream. Submersion was absolute, same for my partner back then. It helped it was 2008 & 2010, we didn't have phones with us.

These days, I can afford to travel in much more luxury but I will always revert to backpacking. It is simply better, more rewarding and intense experience. But sometimes I need to rest after such a vacation :)