Ah I really feel for you and know exactly how you're feeling. I also have 4 between 1-8 years old and go through phases like what you describe. 4 young kids is just hard, you are way outnumbered (my DH also works almost every waking hour) and these are strange times for them as well, don't be too hard on yourself!
How old is the baby? Boundary pushing from the oldest ones is a normal response to a new baby in my experience. This will settle, in the mean time routine helps (and I'm not usually a routiney sort of person).
A couple of specific suggestions which you could try if you haven't already;
Be as diligent as you can with consequences for not listening, it makes a big difference, but it is really tough with a baby so give yourself a break too! You don't have to be perfect!
Get outside as early in the day as you can bare, so hard to get going but has such a positive impact on the rest of the day, even if just a 15 minute runabout.
TV: mine got up at night once and we came down pretty hard on them, tv banned for a while after (this is hard on you too but is worth it if tv motivates them), they never did it again. We also had a phase where we took the remotes upstairs and unplugged to stop them getting up painfully early at the weekend to watch tv, take away the temptation! Generally we have only set times where screens are allowed otherwise it gets out of hand, towards the end of the day so it can be used as incentive.
Engage them in helping with the littler ones where possible, praise their responsibility - e.g fetching nappies, watching / playing with the baby in a secure space while you give the toddler a few minutes attention, help get the toddlers shoes on to go outside etc. Mine respond better when they feel they can be helpful and proud of themselves. Doesn't always work of course but worth a try!
Positive phrasing instead of lots of "no" and "don't do that" really does work better, and making a game of things instead of issuing commands.
Reward charts work but best for one specific thing at a time otherwise, like your example, they tend to drift after a while. I used it most recently for the middle 2 getting themselves dressed in the morning and ready for bed at night without help and chasing. Start with your most difficult time of day to tackle, you can't change lots of problems at once you'll just get overwhelmed!
Build in fun extras that fit what they like/ their personalities. Family reading sessions is tricky with 4 at those ages especially if you have high energy children like me, but garden picnics / film nights/ dance parties / adventure night walks or other ideas may work better. Even if 90% is hard slog a few fun moments, especially if you time these at the end of the day, makes it all feel much better. You can use as another reward system too. Each of mine (except the baby!) have a few small jobs to do in the week which they can tick off on a chart. If the chart is full at the end of the week we do a movie night with pizza all together at the weekend. It has to be realistic though otherwise they will always fail and you'll all feel shitty! Start small...
If at all possible, and I know it's very hard, try to find a few minutes each day for each child one on one, or at least for the older 2 separate from the younger 2 (maybe after they go to bed?) Just to play a favourite game, read a chapter or have a chat. It really helps to bring you closer which should in turn help with the listening.
Regarding taking them out, I have abandoned all thought of taking them anywhere except parks / woodlands or similar for a while! Pre covid we did quite a lot but there were only 3 then and they have lost all social skills through the various lock-downs I fear. Outdoor cafes with a play area work ok but otherwise I'd not be making your life harder than it needs to be for a little while longer!
It is tough but will get better as they all get a bit older, until then find the things that keep you sane and enjoy the few joyful moments when they appear!