The Drow feature says:
Drow Magic. You know the dancing lights cantrip. ...(Other spells)... Charisma is your spellcasting ability for these spells.
Nothing in this ability indicates any modification to the required components. The same is true for the High Elf's Cantrip racial trait, the Forest Gnome's Natural Illusionist racial trait and the Tiefling's Infernal Legacy racial trait. No special exceptions are made for spellcasting granted by these player races.
Contrast this to some of the creatures in the Monster Manual who possess the Innate Spellcasting trait. As a completely arbitrary example, consider the Frost Giant, whose Innate Spellcasting trait includes the line
It can innately cast the following spells, requiring no material components.
The same line is present in the Green Hag, the Night Hag, all four Genies, the Dryad, the Drider, and many, many others. Some creatures like the Mind Flayer and Pixie have stronger exceptions to the components in their Innate Spellcasting traits. However, every single one of them explicitly calls out that it requires no material components (or whatever variant as appropriate).
If the racial spellcasting traits, such as Drow Magic, did not require material components, then the trait would have explicitly said so like the Innate Spellcasting traits do. Rules as written, your Drow does require the appropriate material component to cast the spell.
However, only exceptional circumstances would make this difficult. Your Drow would require only a single piece of phosphorous, wychwood or a glowworm. They could keep it in their pockets, or on a bracelet or necklace or some other piece of minor jewellery (in fact, that sounds like an interesting piece of flavour for races with spellcasting traits). Your Drow would be unable to cast dancing lights if deprived of this material component, but recovering one should be very easy between adventures if not during an adventure.
That said, the GM may rule that Drow Magic functions like Innate Spellcasting and does not require material components. As Miniman pointed out, this would bring the player race's magical abilities to be in line with the Drow which appear in the Monster Manual, which do have the Innate Spellcasting trait. But that technically deviates from RAW.
At will indicates you do not need spell slots.
The rules for cantrips help clarify this language of “at will”:
A cantrip is a spell that can be cast at will, without using a spell slot and without being prepared in advance.
To be clear, the spells from the Svirfneblin Magic feat are not cantrips, but the rules for cantrips give us a clear understanding of what “at will” means with respect to spellcasting.
This is also obvious from the fact that being a spell caster is not a requirement of taking the feat. If the feat required using slots for casting the spells, it would list that as a requirement in some way. The Eldritch Adept feat from UA 2020: Feats, while not official material yet, gives an example of how this would look:
Prerequisite: Spellcasting or Pact Magic feature
This feat would be totally useless to classes without spell slots, unless you can cast the spells without them.
Innate Spellcasting means it doesn’t use spell slots
In the Monster Manual, the Innate Spellcasting trait is given a definition for NPCs:
A monster with the innate ability to cast spells has the Innate Spellcasting special trait. Unless noted otherwise, an innate spell of 1st level or higher is always cast at its lowest possible level and can't be cast at a higher level.
In contrast, the regular Spellcasting trait is described as follows:
A monster with the Spellcasting class feature has a spellcaster level and spell slots, which it uses to cast its spells of 1st level and higher. The spellcaster level is also used for any cantrips included in the feature.
Now, you aren’t an NPC, but this demonstrates the common rules understanding of Innate Spellcasting: no spell slots necessary.
Best Answer
None of the Components—Verbal, Somatic, nor Material—are required for these spells
In the Player's Handbook, in Chapter 10, Spell Components are explicitly described as encompassing the Verbal, Somatic, and Material costs:
So if a feature, like the Githyanki Psionics feature, grants the ability to cast a spell without requiring components (with no further stipulation on which components being specified), that means no components are required; it does not merely remove the Material Components.
This means that such a character would be able to at-will cast mage hand with this feature without verbal or somatic components, and once per day cast jump with no components, and once per day cast misty step without its verbal components.
This only applies to spells cast through this feature; if a Githyanki Wizard had already cast jump through their racial spellcasting, and then tried to cast jump through their Wizard spellcasting, that second casting would still require all the normal components as expected.