What does ‘does not require’ mean?

In this recent question, I asked about Flameskulls and how their Undead Nature interacted with long rests to recover their spells.

In the course of reading an answer, I realized that the poster and I had very different interpretations of what "doesn’t require" means.

Undead Nature. A [specific undead] doesn’t require air, food, drink, or sleep.

(and similar statements for Constructed Nature, Immortal Nature, Shadowy Nature, Elemental Nature, and Ooze Nature)

One interpretation of ‘doesn’t require x’ is suffers no ill effects from the lack of x.

So, for example, since a flameskull doesn’t require air, it is immune to the effects of suffocation (PHB183). Since it doesn’t require food and drink, it is immune to the effects of exhaustion caused by the lack of food and drink (PHB 185). And since it doesn’t require sleep, it would not need to make a Constitution check to go without sleep (PHB177).

Under this interpretation, A flameskull suffers no ill effects from not sleeping, but it still would need to sleep in order to complete a long rest and thus regain spell slots.

A different interpretation of ‘doesn’t require x’ is can accomplish a process without having to use x. Under this interpretation, since a flameskull doesn’t require sleep, it can take a long rest without having to sleep, even though sleep is normally a requirement for a long rest. This would be similar to an elf with the feature of "Trance: Elves do not need to sleep." Even though the general rules for a long rest require sleep, elves specifically do not require sleep to make a long rest.

A similar phrase is used in the description of the flameskull, when it says (emphasis mine)

Spellcasting. The flameskull is a 5th-level spell caster. Its spellcasting ability is Intelligence (spell save DC 13, +5 to hit with spell attacks). It requires no somatic or material components to cast its spells.

Here the ‘requires no’ clearly means that it can perform spellcasting without needing components, not that if it goes without components, it will suffer some ill effects.

While I am sympathetic to this view, I’m not sure it always makes sense. A monk with Timeless Body, for example, "no longer need[s] food or water." If such a monk was multiclassed with druid, could said monk cast Animal Friendship or Animal Messenger without the "morsel of food" that serves as the material component, because they "no longer need" the component of food?

Unfortunately, as far as I know, the meaning of "doesn’t require" is not explicitly defined, at least in the three core source books. As an undefined term, it falls to a natural language interpretation, and both these uses of ‘doesn’t require’ are natural language in different contexts.

To complicate the matter, in the Monster Manual we have

Sleepless. Thri-kreen don’t require sleep and can rest while remaining alert and performing light tasks. Their inability to sleep is thought to be the reason why thrikreen have such short lifespans, the average thri-kreen life expectancy being only thirty years.

Here it seems to equate not requiring something with the inability to do it. Thri-kreen can’t sleep because thri-kreen don’t require sleep. Is this a general principle of what ‘doesn’t require’ means? Not only do elves and flameskulls not require sleep, but that means that they can’t sleep, either?

How are we to understand what a reference to ‘does not require’ or ‘does not need’, means?