How to get my ex back when he is in a new relationship?

Hey! I need some help..

Me and my ex-boyfriend broke off April/May last year. It was a friendly break-up, I mostly lost attraction due to several reasons but also COVID had a big impact on this (mental health). I was the initiator, but he missed the physical side of things too in our relationship. He did say he felt like we were making a mistake, but at that time I felt like we needed some time apart. We kept in touch ever since, because we are on good terms (friends) and we share a dog. In September we still told each other we missed each other but because a lot of things were going on (moving, construction, etc) nothing really came from it unfortunately. I have major regrets about not taking any action back then (but neither did he).

He got into a new relationship 4 months ago and I can’t help but feeling I want him back. Things have changed in our friendship and the way we communicate obviously. When I found out he was dating her (not yet in a relationship) I told him that I wished things were different between us and that I would be open to give it another shot. He was quite firm and said things happened for a reason and basically closed the door. I tried to give up hope but couldn’t, so I blocked him for 2 weeks in January (I explained why) to sort my feelings. I can’t cut him off completely as I need his help with my dog as I travel a lot for work.

After that the two weeks, we established contact again about the dog and now we start building on the friendship side of things again too. He came over for dinner last week and we text each other regularly about daily things in life. Nothing emotional/too personal – he doesn’t mention his girlfriend either (I think to avoid me being hurt about it and I don’t ask). When he came for dinner last time, he did give me a very firm hug at the end.

I feel very mixed – he doesn’t flirt with me in any way (neither do I), out of respect for his girlfriend. Still I can’t shake the hope of conciliation as he does reach out to me and also initiates contact and is open to meet up (even though mostly for the dog). Am I misreading his signals? Does he really only wants to stay friends or is there a chance for me to win him back? I don’t honestly know what I should do to actually win him back. I can’t flirt as there’s a girlfriend involved and I will definitely push him away with it.

Any help/tips?