hi @newf I feel your pain.
Our pup is just a week older and we've been having similar issues. Nights are great; he sleeps in the crate from 11/11.30 till 8. I know we're lucky there! He's still sleepy and docile in the morning and will nap in his bed (crate door open) or the floor and will have another sleep in the afternoon but as you describe, is instantly alert if we leave the room. Although I can cook, empty the dishwasher and that doesn't bother him. He seems to be relaxed as long as we're around.
But our evenings were - and still sometimes are - challenging. Through the day when we're in we live mainly in the kitchen and hall .. both fairly large with wooden floors. After dinner we usually go through to the sitting room to watch TV and that's when he would start to prowl around, chewing furniture, squeezing under it and getting pretty bitey and just unable to settle. Actually he gets increasingly overtired from about 6/7pm. They say make sure your puppy gets plenty of sleep but it's easier said than done. We're providing the opportunity for naps however I think he's just a quite a high energy pup.
The opinion from our puppy class trainer was that the new surroundings were over-stimulating. The kitchen is pretty boring as he's used to it, but the sitting room is full of new smells and textures and corners to explore. So she suggested spending some time in there when he's calm and due for a sleep. I would never have thought of that but it proved to be a great idea. We did that one morning and he and I both fell asleep on the sofa! Having done that a few times it has definitely helped.
What has also worked is making sure he's already calm and tired before we go through there. So he will go out for a wee and a sniff round about 8pm, I put away all the toys and just leave out one chew and a rug, we sit at the kitchen table and more or less ignore him to give him the message that it's time to calm down and he eventually gets bored and settles down. Once he starts to drop off, we give him about 15 minutes to get really sleepy, we walk through and put the TV on, he follows us sleepily and climbs onto his rug on the sofa. He does need a yakker chew/bull's pizzle or similar sometimes to soothe him but occasionally will just curl up and doze.
This doesn't work every night; sometimes we have to go back through to the kitchen and go through it all again but I have hope now that we're on the right track. And hopefully we can extend the time through there as he gets older.
That was a saga! But I hope it helps a bit. It's been our biggest issue so far. If you have any suggestions in return I would love to hear them as we are still very much a work in progress ..