Milk appears to separate from steaming, how do I fix this?

So I’m using fresh, semi-skinned, filtered milk in a cold pitcher. My espresso machine is a Sage / Breville Barista Express. I blast my steam wand before I heat the milk as sometimes the first few seconds are just water out the wand.

I spend the first few seconds adding air to the milk and once it’s thickened a bit and the bubbles have gone, I bury the tip and spend the next 40 seconds or so just heating it until it reaches temperature.

When I pour my milk, the bit that gets to the spout first tends to look very thin and watery and kind of "below" the rest of the milk, running faster. By the end of the pour it’s very thick and frothed.

I’m not sure if this is because the milk has separated somehow, or the steam wand is somehow adding water to the mix or I’m doing something wrong.

How do I get that gloss paint consistency through the whole pitcher?