On intrusive thoughts, I think identifying them early and accepting them is important to re-directing them. It takes lot of patience and practice. Don't give up on the first few tries. Just remember that eventually you will be consistent with your actions.
I am having a horrible day -> what's the least I could do to make this day better? and then do it.
Please don't aim for something you can't do. It's okay if you can get out of the bed. No need to go for run. Aim for the least and gradually increase otherwise you will not do anything due to fear.
Another skill that will help you immensely is ability to prioritize the right things. Writing down what you really should do in order and sticking it to somewhere visible helps.
In the end, no clear solution exist. For some, medication might be the best option and for others, it's lot of training to control the factors leading to intrusive thoughts and eventually depressive episode.
I have also experimented on myself to see whether 30 minutes of exercise improved my mood in the middle of the day. Not totally surprisingly, it _usually_ did. Not always, but usually. It never once had a negative impact.
The main problem is one of motivation/willpower. Telling a depressed person that they should exercise to feel better seems like solid advice on the surface of it, because it stands a high chance of both being true and actually working, BUT they are not in a place to usefully implement the advice. The brain gets in the way and overrides what we see as "common sense." The same way you can't tell an alcoholic to have a nice big steak instead of a beer for dinner. The person usually even knows the "right" thing to do, they are just literally unable to take the right action in the moment.
It's the same for other kinds of exercise. If you're dreading lifting weights, start by just doing some sets of really light reps. If you still feel bad, you can just stop after that, but you'll probably often find at that point that you actually feel like doing more.
Weirdly, I seem to often have my best runs/workouts with this approach, when I started out feeling like crap. Motivation is a strange thing.
I am willing to believe that there are people who won't feel better by going for a run or will be unable to do so, but I think there are probably also people who feel better by simply doing it, even if they don't feel like it.
Especially with depression there also seems to be an ideological battle, were some people absolutely want to believe that it is caused by chemical imbalances and medication is the only thing that can possibly work. (Again, I am willing to believe that such cases exist, but I also think there are people who would rightfully have been classified as depressed who came out of it without medication).
There's a minority of people whom regardless of their circumstances will be depressed. In this case, the argument that a person's monoamine neurotransmitters levels (e.g. serotonin, dopamine, norepinephrine) are just naturally out of whack makes sense and medications might be the best option.
That is not to say that depression doesn't cause more screen time, or worse sleep.
Similarly, if you ruminate on horrible things every time you stop and think, you're going to want to go on your phone late into the night until you're so tired you can go straight to sleep. If you don't even know if life is worth living, it's quite hard to avoid eating that bag of chips. I thought these were obvious, but perhaps it's not to people who've never experienced depression. Perhaps the reductionist view, as unhelpful as it is, plays into it too.