need advice about a player's subclass and whether or not it's too powerful (5e)

[buoyant pier]

Yeah that seems pretty overtuned. An additional rune at level 3 is big. Having five runes by level 7 is a huge boost. That combined with the homebrew runes makes it completely absurd.

Frost rune just a straight up +2 to AC? No time limit? Way too powerful.

Lightning Rune: A 15 movement speed and 3x jump? Mobility is the thing that Monks do best. This makes the heavily armored rune knight more mobile than the monk. No way I'd allow this.

Rune Form: I assume this is replacing giant's might? "Advantage on demand" is very powerful. Would not allow.

My feeling is that Rune Knight is a pretty solid subclass already, and that there's no real reason the player needs any of these changes. These changes are all upside, no downside.

[faint abyss]

Yes, I agree. It's very overturned - RK is already a powerful subclass (everything in Tasha's is). Like, it's really insane. I'm not surprised another player has complained. My general advice is, don't let players do/pick homebrew while you're still learning the system.

Also if we are just straight up comparing it to the monk:
-The RK can now travel faster than the monk, one of the things monks are known for, without spending any resources, while the monk still has to use their features for that.
-Free advantage every turn is absolutely ludicrous. Flanking is an optional rule in 5e, which gives players advantage on a target when they have an ally opposite of said target. Many people either change this to a +2 to hit, or don't use flanking at all, because advantage is a powerful mechanic.

Let's also compare it to the things a kensei monk would get.
Kensei Weapon: They gain proficiency with 2 weapons.
Agile Parry: When making an unarmed strike while holding a weapon, they gain +2 AC until their next turn.
Kensei's Shot: As a Bonus Action, add an extra 1d4 to any ranged attacks until the end of that turn.
Way of the Brush: Gain proficiency with one of two tools.

So you can see how the features the monk gets, and the ones the RK gets are.... disproportional