Shadow Step only teleports you, so you can't bring anyone else (willingly or unwillingly) with you. Compare with other ways to teleport like the spell teleport (PHB, p. 281) which only allows bringing others with you because it explicitly says so.
If you could somehow bring a grappled creature with you through a Shadow Step (a custom Feat, perhaps?), it would not reduce the distance. Shadow Step's distance limit is a fixed 60 feet that is independent of your speed statistic, and drag-grappling only reduces your speed.
On the plus side, the combination of these two points makes Shadow Step a convenient way to escape a grapple against you.
As RAW, no, it does not
Being considered a size higher for carrying capacity and push, drag, or lift force is not the same as being a size higher for all purposes, including grappling.
You count as one size larger when determining your carrying capacity
and the weight you can push, drag, or lift.
As RAI, maybe
The loop hole is that the PHB has no reference on why and how the grapple-er can move without speed penalty if it is two size higher, and the DMG does not touch the subject. There are two potential scenarios for why a grapple-er one size or lower has it speed reduced, though; the grappled creature have enough leverage to make the movement difficult or that the grapple-er cannot carry comfortable enough the grappled creature as in "difficult terrain", and that the weight of the creature is the deterrent.
In the first case, since Powerful Build does not increase per-se the size, it is safe to assume that it does not help to increase the comfort or reduce the leverage and, such, the speed is halved.
In the second case, where is the weight that maters, things change. Powerful Build improves the carrying, dragging, and lift capacity, therefore the grapple-er creature does not have its speed halved.
Which one it is
The only evidence I found is in favor of is that weight is the reason for the reduction in speed. The first part is in the text of moving a grappled creature (emphasis mine).
When you move, you can drag or carry the grappled creature with you,
but your speed is halved, unless the creature is two or more sizes
smaller than you.
As far as I can tell, there are no rules on how you drag or, particularly, carry a grappled creature. You can carry over you head a grapple creature as if it were a sack of potatoes. In PHB 176 there is a segment that shows how can you drag, carry and lift something in particular and, as shown, it is a STR and weight contest in which Powerful Build should work as intended.
Push, Drag, or Lift. You can push, drag, or lift a weight in pounds up
to twice your carrying capacity (or 30 times your Strength score).
Bottom line
At the end is the DM that has the last word. Talk to your DM and present the evidence. If you are the DM decide what it is best for your campaign. If a particular decision is more powerful that you expected it is in your right to take back the decision.
Best Answer
After releasing the grapple, you can move 15 more feet
Movement speed is only halved while you are dragging the creature
The condition is clear, when you move with a grappled creature your speed is halved. If you are no longer moving with a grappled creature, this rule no longer applies and your speed returns to normal.
When your speed changes, the amount you can move also changes
This is a simple rule and it has no qualifiers. During one round you can move up to whatever your current speed is. It doesn't mention any exceptions for cases where your speed might increase or decrease during the turn.
So, the rule simply is:
$$ \text{movementLeft} = \text{currentSpeed} - \text{movementUsed} $$
If your speed increases during your turn (for example if you cast haste on yourself), you can move further that round. If it decreases, so does the distance you can move.
Thus, if you move 15 feet with your grappled creature you have moved 15 feet with a speed of 15.
$$ \text{movementLeft} = (30/2) - 15 = 0 $$ After releasing the grapple, your speed becomes 30.
$$ \text{movementLeft} = 30 - 15 = 15 $$ And, according to the rules, you can move a distance up to your speed on your turn. Since you have already moved 15 and you have a speed of 30, you have 15 feet more you can go.
Haste as an alternate example
Consider the case of haste used mid-turn. Haste doubles the target's speed. Consider a creature that moved up to its current speed, saw a need to move further and then cast haste on itself.
It doesn't make sense for the creature to not be able to move further now that they have a new speed. After all, if they had cast it at the beginning of their turn they would have been able to move the full distance just fine. Why does it matter that they cast it after moving part of the way?
The above ruling correctly (IMO) allows the creature to move the appropriate amount of spaces because movement is continuously calculated off the current speed of the creature. When the speed changes, so does the amount of movement no matter when that change occurs.
Difficult terrain uses a different calculation that does not apply here
Conditions such a difficult terrain use very different rules and language for describing how movement is penalized.
This is not how the moving a grappled creature rules are written at all and they aren't the same as this question demonstrates. Without language like this in the rule for grappled creatures, there is no rules support for calculating the movement the same way. Whether or not this was intentional, only the designers can say. Barring errata, this is the RAW ruling that we have.
As always, if a DM wants to change a rule, they can do so. In this case, changing the rule such that dragging is treated like difficult terrain would probably not be something that has any noticeable effect on game-enjoyment (but it isn't something I've tested).