It’s simply because anything that is present, but incorporeal, on the material plane by definition exists partly in the Border Ethereal. An entity like a ghost, that is tethered to the material plane but has an incorporeal portion, has that part in the plane that is — definitionally — where incorporeal parts of material plane entities exist.
That’s the role of the ethereal plane: being the transition plane between the material and everything else in the planar cosmos. It isn’t primarily the place where “raw materials are turned into the Prime Material”: it only happens to also be that because its foremost nature is being the medium through which the inner planes connect, in both directions.
By contrast, the astral is not adjacent to the material plane, so it’s not a candidate for ghosts’ incorporeal portions. Travelling to the astral plane “naturally” — without portals or spells that take you there — requires passing through the ethereal first. Ghosts are trapped in the border ethereal and can’t even reach the rest of the ethereal plane, because they can’t fully leave the material plane. They certainly can’t reach edge of the ethereal where it meets the astral, and its access to an afterlife in the outer planes.
Playing with planeswalkers
Since you are interested in setting specific features, the simplest way I know of would be to have the party play a group of planeswalkers, using the free Plane Shift Amonkhet supplement (from the Magic the Gathering setting).
It contains an appendix at the end called "Planeswalkers and the Multiverse" that simply allows everyone to travel between planes at any level, (although it is stated that this is recommended for higher level campaigns). This process is then an ability that all players simply have and takes about a minute of focus for a character to travel between planes.
Combining Blink and Banishment
Blink and Banishment, 3rd and 4th level spells respectively, can be combined to allow one to travel to the ethereal plane. Details on how to achieve this can be found in this Q/A.
Since Blink is self only this does require some extra work to do on a whole party (using Glyphs of Warding or Rings of Spell Storing would help), and this is still limited to traveling to the ethereal plane.
Planar Portals
The DMG has a section on Planar Travel which includes Planar Portals as a means of getting to other planes:
Passing through a planar portal can be the simplest way to travel from the Material Plane to a desired location on another plane. Most of the time, though, a portal presents an adventure in itself.
The section contains several more guidelines on what these portals look like, guardians for the portal, etc. In particular, PJRZ suggests hunting out details on the old Planescape setting (Sigil: The City of Doors in particular is all about this!)
This is naturally more of a story element that a DM can introduce rather than something that the players simply decide to do using their own abilities so is also a way for a DM to allow planar travel without giving the players too much power at lower levels.
Best Answer
It seems there are no universal symbols.
The Manual of the Planes from 3.5 edition includes info on Astral Color Pools on page 48:
There is a parallel for the Ethereal Plane, too (as per page 56:
This suggests there is a color theme related to various planes (or, at least, their connecting curtains/pools if not the planes themselves) but as for a specific logo identity or brand for each plane, there is no such indication. All the illustrations are used to try and map out the conceptual relationship of their positions and connections and I could not find where any specific graphic mark is mentioned.
Going further back, to the Planeswalker's Handbook from 2nd edition, we see that the planes are represented thematically.
There is an illustration on Page 7 of the Planeswalker's Handbook that shows a few sketches representing the various planes but there is no text accompanying text confirming or describing the illustration represents anything other than one person/character's choice of representation:
On page 105 of the TSR supplement Planes of Chaos, we find the elements (not the planes) represented thusly:
There are a ton of glyphs here but it's critical to note that this illustration pertains not to the elemental planes but to the elements themselves. The illustration is used in conjunction with the description of how the gods, planes, and elements are intertwined so it's conceivable that some of the glyphs would be used to refer to both the element and its corresponding plane.
Here it's worth pointing out that the Planes of Chaos approaches the lore from the Norse mythology so the symbols it features would not be used by, say, the denizens of a given plane or, say, elves who use a different script.
It then seems to me that, aside from a potential color code given by their connections, representing the planes is left to the imagination of whoever is referencing them and is no doubt informed by that individual's culture. Based on the examples above, though, it would seem that certain general imagery (eg flames representing the plane of fire) is likely common.