The typical concept of innate telepathy is that you just have to "think at something" in a certain way and it happens. You're not casting a spell and using magic, so you don't expect the process to require verbal, somatic, or material components in the way spells do. It just happens.
However, D&D 5e does use spells to describe the inherent mechanics, so, to match the fantasy, it will generally indicate that spell components aren't required. However, there's some confusion when you're using spell slots to power castings.
For example, the final bullet point of the Telepathic feat in Tasha's Cauldron of Everything says:
You can cast the detect thoughts spell, requiring no spell slot or components, and you must finish a long rest before you can cast it this way again. [...] If you have spell slots of 2nd level or higher, you can cast this spell with them.
Similarly, the Githzerai description in Mordenkainen Presents: Monsters of the Multiverse includes the following:
[...] Once you cast shield or detect thoughts with this trait, you can’t cast that spell with it again until you finish a long rest. You can also cast either of those spells using any spell slots you have of the appropriate level.
[...] None of these spells require spell components when you cast them with this trait.
My initial interpretation was that spell components were not required when the spells from these features were re-cast. A spell slot was needed to provide the fuel, yes, but the telepathy was still telepathy, so the character didn't suddenly need to speak gibberish and wave their hands about like a wizard. However, reexamining these descriptions has made me worry that this interpretation does not match the rules as written.
Does the character need to have spell components for the castings that are powered by spell slots? Does the "psionic flavor" vanish after the first casting?