Some good advice here, agree with most. You don't "need" anything per se, but if you "want" (?), a staggered approach makes a lot of sense, especially if budget is a consideration since I think the resale value on your existing devices will be pretty poor (especially the 15" 2019 MBP butterfly kb generation given relative price you probably paid for it).
1) Yes, I think getting a new 16" M1 MBP will feel like a great upgrade from your 15" 2019 MBP. The base 16" M1 Pro (10-core / 16-core, 16gb Memory) with either 512GB/1TB SSD is IMO great value, and also has the best battery life of all the MBP line-up. Will be really nice both when docked, and when you take it with you as a laptop.
2) Next, you could consider getting the Studio Displays. Many thoughts you got above make a lot of sense (especially if you want 2 matching ones, and would prefer not to get 1 at a time). Also as such a new product, might make sense to wait until these get out into the wild and see what reviews say.
3) Lastly, definitely agree that upgrading your iPhone would be lowest priority for me. Especially buying full price / mid-cycle like this, yes you're getting the nice new Alpine Green color, but in 6 months the iPhone 14 will come out and will make yours feel old. Even more so given indications are the iPhone 14 will remove the notch and go with some kind of pinhole/pill cutout, the 13 Pro will "look" older (vs say, 1 year ago, would be a bit less apparent as the iPhone 12s vs iPhone 13s not as big of an exterior difference).
Because the iPhone (and Apple Watch) are updated every year, I think it makes most sense to either buy when it first comes out (so you have the latest model the longest / a full year), or buy mid-cycle at a discount. Buying mid-cycle full price to me feels sub-optimal, all things equal.
