If I have cast something like Animated Objects or Bigby's Hand and then follow up the next round with casting Etherealness, can I still command/control those spells?
Yes for Bigby's Hand; No for Animate Objects and most other spells
In general, nothing stops you from maintaining concentration and continuing to issue commands to the entities created by such spells even from another plane of existence. However, it seems that the vast majority of spells that allow you to issue commands to something require you to be within a certain range in order to issue commands. This is a problem, because as far as I can find, nothing in the official materials defines distances between things on different planes. Jeremy Crawford interprets this lack of a definition as meaning that if two objects are not on the same plane, they are not within any distance of each other. Effectively, the distance between them is infinite. In Crawford's words:
If two people are on different planes of existence, they are infinitely far away from each other. For example, if I'm on the Material Plane and you're on the Ethereal Plane, we're not within 30 feet of each other.
So, Animate Objects says:
you can mentally command any creature you made with this spell if the creature is within 500 feet of you
As long as you are on the Ethereal Plane, you are not considered within this range and are therefore unable to issue commands to the objects you have animated. In contrast, Bigby's Hand has no such limitation. Here are the relevant excerpts from the spell text:
The hand lasts for the spell's duration, and it moves at your command, mimicking the movements of your own hand.
When you cast the spell and as a bonus action on your subsequent turns, you can move the hand up to 60 feet and then cause one of the following effects with it.
There is no mention of any range limitation. As long as you can move your own hand, you can control Bigby's Hand from anywhere on any plane.
Unfortunately, it seems that most spells have limitations that prevent you from issuing commands across planar boundaries, although the nature of the limitation varies from spell to spell. For example, Animate Dead and Create Undead both have a range limitation like that of Animate Objects. Mage Hand "vanishes if it is ever more than 30 feet away from you". Unseen Servant disappears if you command it to perform a task more than 60 feet from you, which means you can issue commands, but any command you issue from another plane will cause it to vanish. Dominate Person has no range limitation, but explicitly limits the telepathic link to the same plane. A zombie created by Finger of Death only obeys commands that you speak verbally, which makes it impossible to issue commands from another plane, unless you have a way to transmit your voice across planes.
In short, you'll need to read your spells carefully, because each one that creates or takes control of an entity has different requirements you must fulfill in order to exert that control, and many of those requirements preclude cross-planar control.
However, your DM could rule otherwise
Lastly, I will mention that as of the 2019 Sage Advice Compendium, Jeremy Crawford's tweets are no longer official rulings. I can't find any official rule that specifically describes how distance works (or doesn't work) between the Material and Border Ethereal Planes, which means that the rules as written leave this determination entirely up to the DM. Crawford's tweet interprets the lack of any definition for inter-planar distance as meaning that things on different planes are never within any distance of each other, but your DM could just as easily decide to fill in the blanks in the rules by defining a distance measure between the Material and Border Ethereal Planes.
Addendum: Indirect evidence of inter-planar distance measure
I only found this much later, and I'm not sure how to integrate it into the rest of the answer, but it turns out while distance between planes is never defined, there are a few instances where official materials assume that it is defined. The description for the Wand of Enemy Detection says (emphasis added):
For the next minute, you know the direction of the nearest creature hostile to you within 60 feet, but not its distance from you. The wand can sense the presence of hostile creatures that are ethereal, invisible, disguised, or hidden, as well as those in plain sight.
If the distance between creatures on different planes was infinite or undefined, then it wouldn't be possible for a creature to be both within 60 feet and ethereal at the same time (assuming the wand's user is on the material plane), so this text would make no sense unless distances between the material and ethereal were defined. Similarly, the spell Mordenkainen’s Faithful Hound says (emphasis added):
When a Small or larger creature comes within 30 feet of it without first speaking the password that you specify when you cast this spell, the hound starts barking loudly. The hound sees invisible creatures and can see into the Ethereal Plane. It ignores illusions.
Once again, the ability to see into the Ethereal Plane would be meaningless unless a distance measure was defined. Unfortunately, these examples still don't supply such a definition, so the DM will need to make a ruling if they want it to be defined.
PHB p. 203 states that the only things that can break your concentration on said spell are when one of the following occurs:
- You take damage and fail a Constitution saving throw.
- You cast another spell that requires concentration.
- You are killed or incapacitated.
The spell in question, Etherealness, states that you cannot interact with creatures or objects that are not on the same plane as you unless they have a special ability or magic allows them to. In this case, since you still have a magical connection to them, you still control and command them.