森を歩く/森に歩く (をvsに)

I see all the time sentenes describing walking climbing swimming, etc through different mediums. Like, for example に (verb)

山に上る

通行に歩く

But I see many instances where they use を (verb), as if they are walking it like a pet or object

such as,,
階段を下げる

川を下る

(Forgive me if my sentences are incorrect, but I wouldnt be asking this question if I wasnt having trouble lol)

How do you know when to use which ? Using google translate, the only nuance I could guess would be the difference of walking along the forest (に) and walking through the forest (を), but not only is GT a little bit sketchy in these areas, but that also isnt a noticible difference at all.

Is there some logic or do I just have to learn case by case ?

Thank you for any responses !

also, is 通行 even being used correctly?maybe 通り would be better ..