Puppy refuses to toilet outside no matter what

My now 15 week old cockapoo point blank refuses to go to the toilet outside. We are taking him outside after every nap, meal, playtime, walk, first thing in the morning and last thing at night, and every 30 mins to an hour between that. We’ve tried waiting outside for 10 minutes at a time, then back in, then out again - he just simply pees or poos when he comes back in. We’ve tried picking him up when toileting inside to take him outside but he continues to toilet despite being picked up, which means even if we grit our teeth through the mess he’s now trailed throughout the house when we do get outside he’s finished doing his business. We’ve tried sprays which are supposed to encourage him to go in certain spots. We’ve tried staying outside with him for hours at a time. Nothing is working. He won’t go when he’s walking either. He doesn’t go even if he’s not been home for a few hours so we know he’ll need it. We’re at a complete loss. I know proper toilet training takes time but my god surely he should at least be willing to go outside when he needs to!?

We know we’re getting our timing right because he toilets when he comes back in from outside almost every time.

What else is there to try!?

We have a puppy pen and are putting him in it between trips outside but he still just refuses to go and then only goes when we let him out of the pen.

I’m pretty much at the end of my tether and I don’t know what else I can do. Any advice anyone has outside of what I’ve already described here would be very welcome, or any reassurance that this is not uncommon and that it will get better… I’m hoping one day he’ll just get it but I’m losing that hope with every passing day.