Should " lightroom ecosystem photos" folder be displayed in lightroom panel

If you have your LR Classic catalog synced with the cloud, what you see in Classic will very much depend on the way(s) that you are syncing. Specifically:

When the Classic catalog is enabled, every image that is added to any of the cloud-based LRCC apps (such as mobile, web, or even desktop) will automatically download into the Classic catalog and thus need to be stored somewhere locally on the Classic system (as was pointed out earlier, Classic can only work with local files, it cannot access the cloud directly). Where exactly those downloaded images are stored depends: the default location will be in some obscure folder name within a folder called "Mobile Downloads.lrdata", usually in the user's Pictures folder, though this can be changed to a user-selected folder (and if desired one of the LR date-based folder schemes).

Whatever storage location is used, the images will be in a folder, and that folder HAS to be visible in the Folders panel, right? If not, they don't/can't be accessed in Classic. If you choose your own location, that folder will appear as a normal folder in the Folder's panel, but if you leave it at the default location then you will see a "drive" appear in the Folders Panel, which will have a name identifying the source device from where the images were originally added to the cloud ecosystem, e.g. I have a couple of "drives" listed on my test system with names like "Jim's iPad", to indicate the file originated from one of my iPads. None of these "drives" will appear, however, if the user uses the preferences to store the synced images in a non-default location.

Within the Collections panel, there may also appear a "From Lr mobile" Collection Set. This will appear if an album is created in one of the LRCC apps, and so syncs down into Classic, i.e. any such LRCC-created albums will appear as collections in Classic under that "From Lr mobile" collection set.

If the concern is the amount of disk space being taken up on your system drive by the downloaded images, simply choose a different location on a different drive by using the preferences. That will not automatically move the images from the default location, however, so the user will need to do that, but do it by working within the Classic's Folders Panel.

To my knowledge, been using LR since Version One, there is no LR Ecosystem Photos folder.

If you are referring to the Previews folder please state that.

I am not certain what you mean by your "ecosystem" folder, but from context it sounds as if you are referring to the containing parent folder for all of your image folders. For example, I have a folder called "library" with all my various year based folders such as "2018" inside that. It's the ultimate target of my new imports and my single point of management for moving to a new drive / backup etc.

Assuming that's what you mean, it is your choice whether to show this in Folders or not - assuming there are no photos living directly within that, only subfolders.

Whenever you want to use it as a point of management, it needs to show.

To stop it showing you can right-click and choose "Hide this Parent". Your next level down folders, now become top level folders (so far as what is visible in LR).

To show it again, you can right-click on one of those current top level folders, and choose "show Parent".