Constrict, Rake and Rend are not natural attacks. They are special abilities that, under certain circumstances, enhance natural attacks. Improved Natural Attack improves the damage of one of your natural attacks (per feat), not one of your special abilities.
Rake and Savage Grapple are pretty similar in effect. Arguably, they could stack, but Savage Grapple is essentially a better effect than Rake (or a better version).
It would be like taking Weapon Focus (Cleave). Cleave isn't a weapon (or an attack), it's a feat that can affect your attack with a weapon.
You could however, have Weapon Focus ([Grapple or Unarmed Strike or Ray]), but these are called out specifically as non-weapon attacks that can be "focused".
Some confusion comes in from the usage of the term "Special Attack" in the monster listings. They have "Special Attacks and Special Qualities"
Many creatures have unusual abilities. A monster entry breaks these abilities into special attacks and special qualities.
However, this is different than what is listed under the combat section as "Special Attacks", such as grapple or bull rush. Specifically, a Special Ability is either extraordinary (Ex), spell-like (Sp), or supernatural (Su). This is where you find Constrict and Rake. Rend is only found in the monster entries, like the troll, but it follows the same format and is listed as
Rend (Ex)
Signifying it is a Special Ability, specifically an Extraordinary Ability.
The Point of Claw Weapons
The point of a Claw weapon is the sharp bit at the end. That is the part you put into your enemy.
All joking aside, Natural Weapons are incredibly versatile and useful for a large number of reasons:
Always there When you Need 'em
One advantage of a Natural Weapon over a manufactured weapon is that you cannot be disarmed (unless you literally lose your arms). If you lose your gear for any reason, you will still be able to hold your own in a fight as you have a lethal weapon readily available at all times.
Not All Claws Are Created Equally
As for the scaling, while not all Natural Weapons scale well into the late game, it just so happens that the Abyssal Bloodrager gets better Claws when you level up. From the Abyssal page:
At 4th level, these claws are considered magic weapons for the purpose of overcoming damage resistance. At 8th level, the damage increases to 1d8 points (1d6 if you are Small). At 12th level, these claws become flaming weapons, which deal an additional 1d6 points of fire damage on a hit.
While these may not be as impressive as a magic weapon at the same level, you get them without spending any gold and the GM will have a hard time getting them away from you.
Size DOES Matter
As per the Universal Monster Rules, a Claw attack on a Large creature deals 1d8 damage. It just so happens that at 4th level an Abyssal Bloodrager may choose to grow one size category (as per the spell Enlarge Person) when entering a Bloodrage. Not only does this increase your Claw damage by one die step (from d6 to d8) but it also grants you +2 to Strength and a reach of 10 feet. This comes with some drawbacks, like a -2 to AC and a -1 to hit, but those are small prices to pay for a really nice benefit.
Full Round Attacks
When you make a full round attack with Natural Weapons you get to apply your full BAB to all attacks made with your primary Natural Weapon and add full Strength on damage.
In addition to this, while you cannot make an attack with a Natural Weapon if you are wielding a weapon in that hand, you can still add an attack from your empty hand (as a Secondary Attack) at only a -5 from your full BAB in addition to all your other attacks for the round. This is essentially a better version of Two Weapon Fighting since it does not require the feat investment.1
Summary
Natural Weapons are incredibly versatile tools for a character to have at their disposal. With the Abyssal Bloodrager's added abilities, the Claw attack will almost always be useful, even if you are wielding a weapon in your main hand. Their damage potential may not be as impressive as a highly magical weapon at a similar level, but they don't cost you any money so you can have your claws AND the fancy magic sword and one of them won't disappoint you when a Rust Monster shows up.2
1: This is my opinion and should not be taken as fact
2: It's the Claws
Best Answer
It isn't overpowered, but it is strong. For example, it allows a Monk to make 3 attacks per round at level 1, or 4 if they are willing to spend a ki point. It's also better damage than any other weapon, as it works out to be (5 + Str * 2) on average vs (7 + Str) for a greatsword.
It's also great for any character that wants to make as many attacks as possible. As an example, Paladins are already known for their nova rounds - now a level 2 Paladin can do (1d4 + 2d8 + Str) * 2 in a single round. It will burn up all their spell slots for the day, but against a powerful monster that they really want to see dead it's definitely going to accelerate their victory.
But where it becomes really problematic is at level 5, when classes start getting Extra Attack. With no interaction specified, this will allow 3 attacks per round for any martial Dragonborn, or 4 if they have a way of getting bonus action attacks (5 for Monks who spend a ki point). Thankfully, this doesn't work with some of the best methods of adding extra damage to every attack, but it will still enable some incredibly high-damage builds.
At level 10, things become problematic all over again, as now every Monk wants to be a Dragonborn, and the claws deal better damage than any one-handed weapon while also enabling more attacks.
To make this non-broken, you need to at least make it require the use of a bonus action, and fix up the interaction with Extra Attack. However, you've said that this feature is in addition to a Dragonborn's normal features. Therefore, rather than making it still strong but not broken, you might want to aim a little lower. I would recommend modelling it off a feature that already exists and represents exactly what you're trying to do: