The rules are unfortunately unclear here
Possess Corpse is listed as an action for the dybbuk and actions are a part of a monster's statistics (see this Q&A for more on what counts as a statistic):
When a monster takes its action, it can choose from the options in the Actions section of its stat block or use one of the actions available to all creatures...
The game uses "stat block" "game statistics" and "statistics" interchangeably so it is clear that the Possess Corpse action is considered part of a dybbuk's statistics.
A monster's statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster. (MM 6)
The problem for the dybbuk is that when it is possessing another creature, it replaces most of its statistics with those of the possessed creature.
Possess Corpse (Recharge 6).
While possessing the corpse, the dybbuk retains its hit points, alignment, Intelligence, Wisdom, Charisma, telepathy, and immunity to poison damage, exhaustion, and being charmed and frightened. It otherwise uses the possessed target's game statistics, gaining access to its knowledge and proficiencies but not its class features, if any.
Actions are unfortunately not on the list of statistics that the dybbuk gets to keep when it is possessing another creature. Thus, they cannot use Possess Corpse while in another body.
However, it is not clear that the Recharge function requires the monster to have access to the ability. The description of the Recharge function from the MM is as follows:
Recharge X–Y. The notation “Recharge X–Y” means a monster can use a special ability once and that the ability then has a random chance of recharging during each subsequent round of combat. At the start of each of the monster’s turns, roll a d6. If the roll is one of the numbers in the recharge notation, the monster regains the use of the special ability. The ability also recharges when the monster finishes a short or long rest.
It is not clear from this if the recharging is just something that happens to the special ability once used or is a feature that requires continued access to the ability. By a default reading the ability recharges regardless, however it is highly unlikely that these general rules were written with this specific edgecase in mind.
Unfortunately, it seems like there is no clear resolution to this except to ask your DM to make a ruling at the table.