Some monsters, like a lich, have the Spellcasting trait. This trait allows such monsters to cast spells using spell slots, much as spellcaster player characters do.
However, taking the lich as an example, the trait does not mention how spell slots are regained (I'm ignoring their Lair Actions for the purposes of this question). Looking at the general rules on monsters' Spellcasting trait in the Special Traits section:
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.
The monster has a list of spells known or prepared from a specific class. The list might also include spells from a feature in that class, such as the Divine Domain feature of the cleric or the Druid Circle feature of the druid. The monster is considered a member of that class when attuning to or using a magic item that requires membership in the class or access to its spell list.
A monster can cast a spell from its list at a higher level if it has the spell slot to do so. For example, a drow mage with the 3rd-level lightning bolt spell can cast it as a 5th-level spell by using one of its 5th-level spell slots.
You can change the spells that a monster knows or has prepared, replacing any spell on its spell list with a spell of the same level and from the same class list. If you do so, you might cause the monster to be a greater or lesser threat than suggested by its challenge rating.
There is no mention of spells slots coming back on a long rest. Elsewhere in the general rules, this is explicitly mentioned for other traits (such as X/Day traits):
For example, "1/Day" means a special ability can be used once and that the monster must finish a long rest to use it again.
It's reasonable to assume that monsters with the Spellcasting trait do probably get their spell slots back on a long rest because that's how it works for PCs, but on the other hand, monsters and PCs don't necessarily use the same rules. So, does anything explicitly state that monsters with the Spellcasting trait get their spell slots back on a long rest?