I'm just going to link this very good and relevant summary of the princes just in case you want some good proof regarding their abilities:
https://forums.spacebattles.com/threads/comparative-analysis-on-daedric-princes-powers.380167/
"You think that, because you perceive a superficial resemblance between the outward appearance of the Nightmare Courser and the Hell Hound, that they must share a 'relationship.' Ever the mortal mind defends itself against the reality of what it cannot comprehend by the pathetic imposition of familiar patterns on entities of inconvenient hyperagonal morphology. Bah. Reflect on the fact that you have failed to understand a single word of my explanation, and burden me with no more such questions." - Lyranth the Foolkiller
"Know that there are places beyond Tamriel where the cunning and the wary can go to learn forgotten spells. I speak of the planes of Oblivion. The sea of limitless dimensions contains an endless series of islands. Some are controlled by the mighty Daedric Princes; others are loosely connected to one minor Daedra Lord or another. On these islands, creatures dwell who possess secrets out of time. Some are there of their own volition, but others are banished there for crimes either heinous or imagined." -Rulantaril's notes
The relevant bit of liminal bridges: "Transliminal passage of quickened objects or entities without the persistent agency of hyperagonal media is not possible, and even if possible, would result in instantaneous retromission of the transported referents. Only a transpontine circumpenetra- tion of the limen will result in transits of greater than infinitessimal duration.
Though other hyperagonal media may exist in theory, the only known transliminal artifact capable of sustained transpontine circumpenetration is the Sigil stone. A sigil stone is a specimen of pre-Mythic quasi-crystalline morpholith that has been transformed into an extra-dimensional artifact through the arcane inscription of a daedric sigil. Though some common morpholiths like soul gems may be found in nature, the exotic morpoliths used to make sigil stones occur only in pocket voids of Oblivion, and cannot be prospected or harvested without daedric assistance.
Therefore, since both the morpholiths and the daedric sigils required for hyperagonal media cannot be obtained without traffic and commerce with Daedra Lords, it is necessary that a transliminal mechanic cultivate a working knowledge of conjuration—though purpose-built enchantments may be substituted if the mechanic has sufficient invocatory skill. Traffic and commerce with Daedra Lords is an esoteric but well-established practice, and lies outside the compass of this treatise."
Hyperagonal is a term referring to degrees of freedom perpendicular to 3-D movement. It essentially refers to higher dimensions. True it is not specific as hyper denotes any higher dimensional space, but the limitless dimensions thing should sum it up. Also the argument that dimensions mean universe is invalid as islands appears to refer to universes otherwise it would be a tautology. Dimensions is a property of oblivion hence "the sea of limitless dimensions"
Based on evidence providee for other characters regarding higher dimensions i think this is sufficient to say daedric princes are definitely higher dimensional 100%