"Giving their main character sneak attack" is not as overpowered as you think. Rogue's party is expected to position for his sneak attack each turn; this only helps him to do it by himself, somewhat lessening potential teamwork. Are there any social disadvantages for walking around with spooky shadow creature in tow? Spellcasters are already frowned upon by a part of population.
I have a limited experience with 5e (I assume you're playing 5e version of the campaign), so take the following with a grain of salt. Reading through the subclass, it's a weird combination of echo knight and shadow sorcerer with a touch of warlock.
The main problem is with Shadow's attack, +4 to hit, 2d6+2 necrotic, with no scaling at all. The author probably intended raising its Dex score to increase to-hit modifier, but it's not written anywhere, and it lacks scaling proficiency in either case. So it's above expected DPR at lvl 3 and then progressively gets weaker and weaker with each level, and other subclass features do nothing to remedy that.
If I were to fix it... First of all, talk with the player. What's his expectation of this subclass?
- Is the shadow his equal, the main source of his menace (summoner fantasy, your companion attacks enemies)? Beast master Ranger could be a template for this, with scaling stats. Probably allow the shadow to sneak attack in place of the rogue himself once a round, or add some limited "shadow smite"-like damage burst options at later levels.
- Or is it a spooky guest from the Shadowfell, who grants rogue a portion of his power (somewhat like a patron to warlock)? High level features (teleport and invisibility) fit this well. Not sure how the shadow companion would work in this case tbh; maybe look at warlock invocations and grant some every 4 levels? But there's not much synergy with base rogue abilities there, I'm afraid.
- Or maybe it's not powerful by itself at all, like a weird pet, which is useful, but not threatening (like a wizard's familiar). Echo knight's "shadow" would be a good template for this variant: it's vulnerable (1 hp) but resummonable, provides great mobility and area control, but a limited increase in damage.
In all cases, take notice that this subclass functions extremely poorly at bright light (or maybe only in sunlight, a bit unclear). This can be remedied with a granted cast of
darkness (once a day?), but I'm not sure how to power budget it.