TL;DR, this subclass is moderately underpowered
This subclass appears to most comparable to the Oath of Redemption in that it has both a non-combat and a combat Channel Divinity, a largely defensive level 7 and level 15 feature, and largely defensive or non-combat Oath Spells. As such, I will be comparing to that oath for this balance analysis.
The Level 3 Oath Spells of jump and catapult are slightly stronger than the Redemption Oath Spells of sanctuary and sleep.
Jump and sanctuary are both situationally useful, but Jump is slightly more widely applicable than sanctuary, but not enough to designate a pro.
Catapult and sleep are both solutions to something the paladin is less focused on (ranged attacks and condition-inducing respectively). Sleep is very efficient against low-level opponents and falls off in higher tiers. In contrast, than catapult is a useful option for those paladins who dump dexterity throughout every tier. That grants a slight pro over Oath of Redemption.
Your subclass falls short a little here.
The Redemption Paladin's non-combat Channel Divinity, Emissary of Peace, is very widely applicable, while Sense Alignment is very niche. This is a moderate con of the Oath of the Jedi to the Oath of Redemption.
As for the combat option, Repelling Blast is quite strong at early levels, but begins to fall off as the paladin start dealing with stronger threats. In contrast, Rebuke the Violent of the Oath of Redemption scales based on the damage the enemy does. This makes Repelling Blast a slight con compared to Rebuke the Violent (only slight since it is quite strong in the early levels).
Overall, the level 3 Oath of the Jedi features are moderately weaker than the level 3 Oath of Redemption ones
The level 5 Oath Spells of blur and detect thoughts are about equal to those of the Redemption Oath Spells of calm emotions and hold person.
Blur and hold person are both potent combat options, while calm emotions and detect thoughts are both non-combat challenge solvers (for negotiation and interrogation respectively).
The level 5 Oath of the Jedi feature is balanced compared to the level 5 Oath of Redemption one
Unarmored Defense is a quite potent feature, but the usage of Wisdom handicaps it a large amount. This is especially true since paladins already need many different ability scores with Strength or Dexterity for attacks, Constitution for hit points, and Charisma for Spellcasting.
The Oath of Redemption's Aura of the Guardian is a moderately useful ability for ensuring that the less durable party members can take less damage. Because Unarmored Defense is only slightly useful with its focus on Wisdom, it is a slight con when compared to Aura of the Guardian.
The level 7 Oath of the Jedi feature is slightly weaker than the level 7 Oath of Redemption one
The level 7 Oath Spells of wind wall and protection from energy are about equal to those of the Redemption Oath Spells of counterspell and hypnotic pattern.
Wind wall and hypnotic pattern are both spells that affect the battlefield as a whole. Wind wall deals decent damage and is a potent defensive spell against ranged attacks, while hypnotic pattern is a potent condition-inducing area of effect spell. They are relatively balanced against each other (although hypnotic pattern is a bit better, it is not enough to warrant a con).
Counterspell and protection from energy are both defensive options against particular kinds of opponents. If paladins had more spell slots, counterspell would be more useful than protection from energy, but as is they are balanced against each other.
The level 9 Oath of the Jedi feature is balanced compared to the level 9 Oath of Redemption one
The level 13 Oath Spells of freedom of movement and divination are about equal to those of the Redemption Oath Spells of Otiluke’s resilient sphere and stoneskin.
Freedom of movement and stoneskin are potent defensive options against particular opponents (some condition-inducing ones and those that deal nonmagical bludgeoning, piercing, and slashing respectively). However, at this tier, stoneskin is not quite as useful as it would have been at level 9 when other casters get it. This is a minor pro to the Oath of the Jedi.
The mileage a character can get out of divination is very dependent on the campaign and the GM. That being said, it is typically a moderately useful spell in my experience. However, Otiluke’s resilient sphere is very useful even at this later tier. This is a slight con to Oath of the Jedi.
Overall, the level 13 Oath of the Jedi feature is balanced compared to the level 13 Oath of Redemption one
Improved Mind is a twofold feature. The psychic resistance is a fairly minor benefit when compared to what the Oath of Redemption offers. That being said, the improvement to Sense Alignment is very powerful, but it is still tied to the Channel Divinity and the Wisdom ability, significantly hampering its impact.
Protective Spirit doesn't provide the most stay in battle among similar features, but it still is moderately more powerful than resistance to a single less common damage type. With the Sense Alignment improvement, Improved Mind is just a slight con compared to Protective Spirit.
The level 15 Oath of the Jedi feature is slightly weaker than the level 15 Oath of Redemption one
The Level 17 Oath Spells of telekinesis and steel wind strike are slightly weaker than those of the Redemption Oath Spells of hold monster and wall of force.
Both telekinesis and wall of force are widely applicable spells that provide the option to disable opponents as well as a number of creative uses. They are balanced against each other.
On the other hand, hold monster is one of the more potent disabling spells in the game. This is a slight benefit over steel wind strike which, while a good one, is just a damage option.
Overall, the level 17 Oath of the Jedi feature is slightly weaker than the level 17 Oath of Redemption one
One with the Force is slightly stronger than Emissary of Redemption. It provides a similar defensive bonus in the Dodge bonus action as the resistance to attacks, but resistance is slightly more widely applicable (especially in the top tier). The damage component is also much stronger from the Oath of Redemption dealing half of the opponents damage back to them.
That being said, the Oath of Redemption loses these benefits if they attack or deal damage to a creature. As such, One with the Force is overall slightly stronger (blindsight and death saving throw advantage are only minor benefits at this tier; not quite enough to push it to a moderate pro).
Overall, the level 20 Oath of the Jedi feature is slightly stronger than the level 20 Oath of Redemption one
Overall, the Oath of the Jedi has 4 points worth of cons to the Oath of Redemption. These are as follows:
- 2 points at level 3 due to the weaker and more narrowly-applicable Channel Divinity options (counteracted somewhat by the usefulness of catapult)
- 1 point at level 7 due to the lesser defensive feature, and Channel Divinity limit on the Wisdom attack bonus.
- The one pro and one con in the 4th tier cancel each other out.
I would recommend changing the features to use Charisma instead of Wisdom, this would solve the problem of the level 7 feature, by making Oath of the Jedi slightly stronger than Oath of Redemption at that level. I know Wisdom is connected to the flavor of the jedi, but since the oaths are tied to Charisma, it is a better fit.
Hitting the slightly stronger level 7 feature makes the lack of scaling of Repelling Blast acceptable for the subclass overall.
With this done, the only step is to improve the scope of Sense Alignment. It needn't be as ubiquitous as Emissary of Peace (and making it so may unbalance the level 3 features as a whole), but if its a bit less niche you'd have a balanced subclass.
Alternatively, you could keep the niche of Sense Alignment and make Repelling Blast scale somewhat better so that it is a compelling Channel Divinity option at later levels.
Overall, this is a very creative, flavorful and well thought out subclass. It is very close to balanced, and I think with just a few small tweaks it would be ready for playtesting. When playtesting focus on making sure the features work the way they seem to in practice, and ensure that the Oath Spells feel impactful and fit the flavor of the Sacred Oath. I suspect that this subclass will do great.