Keep at it.
I have a 7 month old springer who was/is exactly the same - would scream the house down when I left the room, even if he was with other people in the family. Never cared for kongs or treats or anything left to amuse him.
He still gets left in a variety of circumstances several times a day. e.g. I feed him breakfast then pop upstairs to brush my teeth etc. I answer the door with him shut in the kitchen. I pop to the shop and leave him alone. He has to get out the bathroom when I want a wee. He has to stay downstairs if I need to pop up for something. We have baby gates on all main access points so sometimes he has to stay behind one while I am in the next room (e.g. behind the gate while I am cooking or in the kitchen when he is muddy and I am in the lounge). We just keep going.
About a month or so ago I noticed his crying changed from something that sounded like genuine worry to more a half-hearted type cry. He also started to give up crying more easily. Sometimes now he doesn't make any noise at all. About the same time I noticed he started to take himself off the sleep - for example, if we are all in the lounge in the evening he often wanders off into the kitchen to sleep alone because he prefers the cold floor. As I type he has wandered downstairs alone to get a drink and play with a toy.
When I leave the house completely he still howls, cries and generally gets himself into a pickle. I am only gone 10 mins but I started filming him while I am gone. More and more I notice little moments where he shuts up and lies down. They might only last 10 seconds before he is up and pacing/crying again but they are there more and more.
It's got to the stage where I am thinking about leaving him a bit longer to see how he does.
I was talking to a friend the other day who had massive issues with their cocker who would get herself into a real state if left as a puppy. She would poo, trample in it and they would come home to find her really very distressed - even if left for a short while. When I asked how they worked through it they said that persistence paid off. They never left her very long but kept leaving her and when she was about a year old she was fine. She is now a 12 year old dog who you would never imagine ever worried about being left alone - she is fine left almost anywhere and will just settle down, sleep and wait.
It's true that some dogs do suffer terribly with anxiety when left and require a different and more gentle hand to training to be alone. However, on the face of it, I would guess your pup is just going through the normal development phases.