Here's a meta analysis[1] from 2012 showing that walking has a strong positive effect on depression. Here's one showing that biking and walking for commuting were associated with improved physical/mental health[2]. Here's a newer study showing benefits to the elderly from walking in urban green spaces[3].

Seems like a well supported idea.

[1] https://www.sciencedirect.com/science/article/abs/pii/S17552...

[2] https://www.sciencedirect.com/science/article/abs/pii/S01604...

[3] https://www.frontiersin.org/articles/10.3389/fpubh.2020.5759...