I'll start this off by saying I struggle and have struggled with depression for most of my life, and damn do I passionately hate running. Running is just objectively a painful experience.
Even though running may be a lung-burning experience, deep down whenever I go on a run, I almost instantly feel better about myself. I honestly don't truly understand much of the science behind why I feel better after running, but I can damn well notice the difference. It's not massive, It's not like I run a mile and then wow all I see is sunshine and rainbows. Truly it just boils down to the fact that afterwards I just feel better about myself, I feel more comfortable and relaxed, and also feel like I accomplished by doing something meaningful after I run.
This idea can be linked to all forms of workout in my opinion, for me personally I feel like running just has the biggest effect. I think running has the biggest effect because I dislike it the most, so whenever I do run, I really feel like I accomplished something.
Another big reason why I try to run when I'm having a bad day is because even if my running doesn't actually make me feel better, I'm at least getting in shape. Essentially I'm locking myself into a win-win scenario, either I run and start to feel better, or I run and my cardio health gets better. Really the only downside to running is the fact that I actually have to run to achieve this, and like I said earlier, running is just absolutely awful.
Discounting the fact that running is a great way to make your ankles hate you, running is an incredibly effective way of making you feel better. So even if you hate running as much as I do, give it a shot sometime, you might love the outcome.