UPD

I’ve recently discovered that the issue I’ve been reporting is actually a known problem among players and is commonly referred to as the “Illithid Persuasion bug.” I regret not identifying it under this name earlier.

The bug is even mentioned in the official BG3 Wiki:

“Normally, this power is automatically granted to all tadpoled companions. However, if a companion is convinced to use tadpole powers while not in the active party, a bug will prevent the ability from being granted. This forces the player to spend an extra tadpole to unlock their progression. This does not occur when the companion is in the active party as they are being convinced.”
Source: https://bg3.wiki/wiki/Illithid_Persuasion

Additional player reports also confirm the issue:

• https://www.reddit.com/r/BaldursGate3/comments/1d9005s/illithid_persuasion_bug_help/
• https://steamcommunity.com/app/1086940/discussions/3/3880470762769752397/