Healing means the recovery of hit-points
While the above sentence is never spelled out verbatim, I want to make my case that when read with full context, the Player's Handbook is clear about it.
The first sentences in the section "Healing" in the PhB says:
Unless it results in death, damage isn't permanent. Even death is reversible through powerful magic.
And the section about Hit Points says:
Whenever a creature takes damage, that damage is subtracted from its hit points.
Damage is a game term that is linked to the subtraction of hit-points, and healing is linked to the reversal of damage.
The "Healing" section also says
When a creature receives healing of any kind, hit points regained are added to its current hit points.
I have seen arguments that this concedes that healing does not necessarily regain hit points, but I disagree. It neither implies that healing regains hit-points nor does it imply that healing doesn't imply regeneration of hit points. It merely says what to do with hit points regained when healing.
The section "Death Saving throws" in the Player's handbook says
The best way to save a creature with 0 hit points is to heal it. If healing is unavailable, the creature can at least be stabilized
This says that healing a dying creature is better than stabilizing, but it does not further specify why healing would be better than stabilizing. I believe the reason is obvious: it's because it is clear that "healing" refers to recovery of hit-points, which means that the dying creature would be brought back from 0 hp if it received healing.
So, I argue that "healing" seems to be a game term that refers to hit-point recovery. Spells like "Lesser Restoration" or "Greater Restoration", which recover statuses but not recover HP, may be perceived as "healing" when parsing it in the natural language sense, and they are tagged with "Healing" in databases like DnDBeyond, but I believe that in the game mechanics these are not actually "healing".
But RAW is ambiguous on whether receiving zero healing counts as receiving healing
While it seems clear to me that healing refers to the recovery of hit points, what's not clear in RAW is whether healing that has been reduced to 0, should still trigger effects that are triggered by healing. The same goes for receiving damage, btw.
This Sage advice (which is considered canonical), is often cited to show that damage reduced to 0 should still count as damage:
There is not a damage minimum of 1, so it is possible to deal 0 damage with an attack.
However, I would argue that this is a misreading. The above quote was an answer to the question whether it is possible to reduce damage to zero. The question was, whether effects that reduce damage are allowed to reduce it all the way, or whether they would only be able to reduce it to 1. The answer is, that these effects are allowed to reduce the damage to 0. It does not, however, say that receiving 0 damage would still count as receiving damage for the purpose of triggering effects that are triggered by damage.
Clues to RAI imply that healing 0 hit points does not count as healing
Jeremy Crawford's tweets may not be RAW, and his rulings are not rules, but I think his tweets still give insight into RAI.
Taking 0 damage is the same as taking no damage.
If you took no damage, you didn't take any damage.
This was in response to a question about whether 0 damage would trigger CON saving throws for concentration. I think it is clear that JC thinks 0 damage does not trigger effects that are triggered by damage. I would extrapolate from that, that in JC's view 0 healing should also not trigger effects that are triggered by healing.
Furthermore, as this answer points out, it would be intuitive to assume that the two abilities of the monster should be in synergy.