Force Ghosts are complicated, to say the least. That might not seem immediately obvious, seeing as how ghosts in Star Wars are just the souls of the dearly departed. Jedi, being attuned to the Force, merge with it upon the event of their demise, becoming one with it.
However, inevitably, the longer a concept becomes embellished by and elaborated upon by numerous different writers with different perspectives, things become complicated. Inevitably, fans have noticed elements about Force Ghosts don't necessarily add up or entirely make sense. These questions have led to many valid questions pertaining to how Force Ghosts work.
A MATTER OF ANATOMY
In theory, a Force Ghost looks like how a person looked upon the instant of their death or when they were last closest to the Light Side of the Force. Anakin Skywalker, for example, returns as a Force Ghost as either a fully-healed version of himself upon the time of his death or as his prequel, pre-Dark Side self, depending on whether you're watching the Original or Special Editions.
However, many viewers had questions about Luke Skywalker's force ghost. When Luke appears in The Rise of Skywalker, his robotic hand isn't visible, with it often being covered up by his robes rather than exposed, as Reddit user xraig88 pointed out. This, of course, makes one wonder how Luke, as a Force ghost, would have a robotic hand?
This also brings up a lot of issues about the physicality of ghosts. Yoda, for example, hobbles and moves as he did as a sickly, elder man when he returns as a spirit in The Last Jedi, not as the flexible, spry Jedi who could engage with Palpatine in the prequels. Similarly, Obi-Wan appears not as a young Jedi Knight but as a wizened hermit. Contrary to that, however, is the spirit of Anakin Skywalker. Darth Vader's Force Ghost has four limbs too many, being recovered in his physical prime rather than a battle-damaged hero.
ARE FORCE GHOSTS EVEN PHYSICAL CONSTRUCTS?
The relationships Force Ghosts have with the material world is tenuous at best. Late last year, a rough draft of the script of Return of the Jedi revealed that, at one point, Lucas planned on Obi-Wan and Yoda's Force Ghosts coming to combat Palpatine in his Death Star throne room. This idea went unused, but it proposes the possibility that Force Ghosts can interact with the living world.
In the sequel trilogy, however, Force Ghosts take on a more active role. Yoda is able to blow apart a tree in The Last Jedi and Luke can catch a lightsaber in The Rise of Skywalker. They are an embodiment of the Force, which explains why they can use force objects and interact with objects -- but only, seemingly, objects sensitive to the Force or on highly force sensitive planets like Ahch-To.
This also ties back to the matter of the mechanical limb. Force ghosts can manifest clothing, but can they also manifest machinery? If so, is it separate from the Force Ghost or a part of their being, like clothing? Ultimately, none of this is crucial to the story at hand, since these ghosts might not be manifesting physical constructs at all, but rather the image of physicality.
THE SELF PERCEIVED BY THE SELF
One interesting possibility is that Force Ghosts don't materialize based on how a person truly is. Rather, the ghosts manifest how the Jedi perceive themselves. Yoda had been a physically frail Jedi on Dagobah and had remained that way for years. To him, he perceived himself as that old, wild hermit.
However, Vader's Force Ghost indicates a truly complicated psyche. As Obi-Wan states, from a certain point of view, Darth Vader destroyed Anakin Skywalker. Ergo, the Anakin Skywalker seen in Return of the Jedi is a representation not of Anakin as he was at the time of his death but of the version of himself that was killed by Vader. Anakin was slain by Vader the moment he killed Mace Windu, long before being burned and maimed on Mustafar.
With all that in mind, the only logical conclusion here is that the Jedi manifest the way they see themselves, complete with the clothing they choose to wear and the forms they take on. This holds true with Force Projections as well, since Luke's hair is far darker in his Force Projection during The Last Jedi than it is throughout the rest of the film. Ultimately, this means Force Ghosts exist as a conditional concept without any regulated, consistent standards. They are, like the Force itself, fluid.