Welcome to the community, or at least welcome to posting as it seems you have at least been reading here? I am so sorry to hear about Tony. There really is something deeply painful about losing a beloved animal family member.
When I lost one of my cats in 2015, it was very hard because he was definitely like a child to me. He was smart, engaging, expressive, and always wanted to be with me. I wasn’t clean/sober at that time, but one of the things I did to help me grieve was to get some photos printed of him and put them in a frame. I wrote down my feelings, and I let myself cry.
Today my other cat is 21 and has always been more like a good friend/room-mate than a child to me until the last couple years. We have had a couple of very real health scares in the last few years. Each time I began the grieving process as it looked like we would need to say goodbye only to have her make a come back.
I have often asked myself how I will deal with the grief when she does finally pass. The amount of time and effort I put into her care on a daily basis is bound to make the loss even more impactful. My daily routine and sleeping schedule is literally crafted around her feeding and medications.
Since you work out, it might help to plan for extra time to do that, since exercise can be a really great way of expending extra emotional energy. Let yourself cry and let it out. There are people who will mock the idea of deep grief over a pet. If you have people like that in your life, don’t confide in them with this, and don’t tell yourself that you should be “over it” by now. You won’t ever be “over it”, but time will lessen the sadness.
If you have a schedule, stick to it. If you have specific times you do things for Tony, such as feedings, litter box scooping, play time, petting and cuddle times, etc., you will inevitably feel that deeply because those things are “habits”, and breaking habits is a very uncomfortable thing in general. Decide on little behaviors you can implement in place of those habits, that way there will be no “empty time”. “Empty time” can be filled by unhealthy behaviors unconsciously sometimes.
If it is helpful, you can post a picture of Tony in the cat thread in the community and tell us something about him at times you are really missing him. Sharing stories of a lost loved one can sometimes be helpful. If you have friends or family you are close to, doing this in person can be helpful. Some people also find it helpful to make a little “pet shrine” for a time. Having a candle that you light at such a place may also prove useful. Let yourself fully grieve before getting another cat, if you plan to. Maybe volunteering at a local pet shelter could prove useful.
Going to a meeting could also be helpful if you really feel this loss affecting your sobriety. If you don’t like the group you find, you can find another to attend. Being more active on this forum or another one may also be helpful for sobriety’s sake as it gives you something to focus on. Focusing some of your extra energy on personal care, more than normal, might also be beneficial.
Losing a beloved pet is never easy. I’m so sorry you are facing this inevitable loss. I hope you will be able to find some comfort in this difficult time.
Edit: If you are able to do it, having someone come to your home to let Tony pass is a nice option. It is more expensive, but he will reach the clearing at the end of the path at home, where he has been happy, rather than at a cold and foreign vet office. I personally found this to be more emotionally soothing as well.