Psychic Blades
The Soulknife from Tasha's Cauldron of Everything gains the Psychic Blades feature at level 3. These are described as "shimmering blades of psychic energy . . . that you can manifest . . . from your free hand." Their description goes on to say [TCoE, pg. 64-65]:
This magic blade is a simple melee weapon with the finesse and thrown properties. It has a normal range of 60 feet and no long range, and on a hit, it deals psychic damage equal to 1d6 plus the ability modifier you used for the attack roll. The blade vanishes immediately after it hits or misses its target, and it leaves no mark on its target if it deals damage.
After you attack with the blade, you can make a melee or ranged weapon attack with a second psychic blade as a bonus action on the same turn, provided your other hand is free to create it. The damage die of this bonus attack is 1d4, instead of 1d6.
Underwater Combat
In underwater combat, weapons are typically subject to limitations that appear to be mimicking how water resistance (or "drag") acts on the weapon or on the wielder's body [PHB, pg. 198]:
When making a melee weapon attack, a creature that doesn’t have a swimming speed (either natural or granted by magic) has disadvantage on the attack roll unless the weapon is a dagger, javelin, shortsword, spear, or trident.
A ranged weapon attack automatically misses a target beyond the weapon’s normal range. Even against a target within normal range, the attack roll has disadvantage unless the weapon is a crossbow, a net, or a weapon that is thrown like a javelin (including a spear, trident, or dart).
What the Rule Mechanics Appear to Say
Underwater Melee — Because a psychic blade is not "a dagger, javelin, shortsword, spear, or trident," a soulknife rogue without a swimming speed will wield it with disadvantage.
Underwater Ranged — The psychic blade's ranged attack roll will be at disadvantage unless it's "thrown like a javelin." Since it's unclear how exactly the blade is thrown, this will be up to DM interpretation.
What Seems Right
Underwater Melee — The psychic blades are "a simple melee weapon with the finesse and thrown properties," so they're most similar to daggers. We therefore apply the improvised weapon interpretation [PHB, pg. 147] and treat them as daggers for the sake of this rule. Thus underwater melee attacks with them are not at disadvantage, regardless of whether or not the soulknife rogue has a swim speed.
Underwater Ranged — Since the psychic blades are "made of psychic energy," there should be no resistance to their movement when they're thrown. Therefore they're treated more like underwater ranged attack spells, with the blades not thrown at disadvantage underwater.
Questions
Do my descriptions under "What the Rule Mechanics Appear to Say" match your understanding of the Rules As Written? Is there any indication that "What Seems Right" describes the Rules As Intended? Or is there yet another interpretation I should consider?
Best Answer
RAW - Psychic blades suffer disadvantage when used for melee or ranged attacks.
Psychic blades are not daggers, javelins, shortswords, spears, or tridents. If they were the rules would say so. Hence, strictly speaking, they would suffer disadvantage when wielded as melee weapons underwater.
Ranged attacks are bit more ambiguous but the description does say its a "blade", which is...well...blade shaped. i.e. it does not have a long thin shaft which would be required to be "thrown like a javelin" and so would also suffer disadvantage when used for ranged attacks underwater.
(I would also disagree on your fiat statement that "psychic blades are "made of psychic energy," so there should be no resistance to their movement when they're thrown" on the basis that there are no physical rules, either in D&D and obviously not in real life, on whether psychic energy has movement resistance underwater!)
However...
All that said, I would totally accept a DM that ruled otherwise, partly for the reasons you've argued in your description (a finesse weapon implies it's light and wieldy enough to be used underwater) and partly for fun/balance reasons (another character could possibly switch to a different weapon but a soulknife's blade is kind of their "thing" so may be more frustrating for them compared to other party members).