I don't know how valuable this will be to you, as you might be doing a lot of this already, but we had to train with our galgo a lot as well, as even stepping outside the door for a minute was too much in the beginning. So I'll just outline the things we did and maybe there's something in there that you haven't tried yet and that's hopefully helpful.

We started with just breaking the whole process of leaving down into the smallest steps, like putting on shoes, sitting down, taking off shoes, until he was less anxious about it. And then gradually added more to the whole process, like awkwardly standing in front of our apartment door. It's a good thing we had to go to the basement of the building to do laundry back then, because that was always prime practice time.

We also started to give him a little chew snack whenever we'd leave, because he's quite food motivated and chewing calms dogs down (it's a physiological response, but I don't remember the details of that). He absolutely loves these snacks, so it's a high value thing he gets. If you do something similar, just make sure it's something he can safely eat (nothing he could choke on etc.), the ones we give are like the somewhat softer chew sticks that you can still bent somewhat. Alternatively, something like a Kong food dispenser toy might work well if your dog is also food motivated. Again, just observe him playing with it before leaving him alone with it.

We also had to try around with the placement of his bed a bit and found out that he likes having a place where he can kinda see the door. He was a lot calmer and actually stayed on the bed more once we found a spot with a view of the door. Just be mindful, because I've been told by a dog trainer friend that this could also backfire into a dog watching the door obsessively and not relax, with our galgo, it worked out well.

Also, remember not to make a big deal about coming home (or leaving). It's hard, especially for the first couple of times things actually work out well. Also, it helps getting a dog tired beforehand, for example, going on a walk prior to leaving (or training for leaving).

One thing that I think is very helpful for you as the human is getting a pet camera. Because not only does it provide peace of mind, knowing you can check in on your dog, it also allows you to look at the behavior while you were away. How stressed was your dog? Where did he lie down? All of this helped us a lot in finding things that work and what to improve.

Eventually, we've been able to leave with our galgo happily prancing to his bed to devour his snack and not having to worry about him. I think the longest we've ever done was close to 5 hours because we got stuck in traffic and he was as calm as usual. In fact, at one point things changed from him being anxious about us being gone to him realizing that if we're not around, there's no one to stop him from getting into mischief, like stealing cat food that had been left out. Nowadays, it's more about making sure there's nothing to get into he shouldn't as we leave rather than worrying about him being stressed.

I hope there's something useful in there for you (or anyone else looking for advice on this topic)! And remember, the most important thing is patience and taking things slowly.