I’m stuck

Has he seen a doctor?

Criticizing isnt the way. If he feels like music and video games help him take off his mind then why not try to use it to help like playing together or putting on music you both like and dance and turn it into somethinf you both enjoy.
Getting someone to see a therapist is hard. Took me years. Someone needs to recignise he needs help and that therea no shame in doing so.
Have you maybe asked a therapist or councelor about how to best cope and encourage him?
Find things you both can do together and show him you are there and love him no matter what comes and keep praying. You can fast too.
Please keep us updated

My husband suffers from severe anxiety. He wakes up everyday throwing up because of how bad it is. Idk what to do for him, I ask him to pray with me or to read his bible and he won’t. I pray every single day for him and for god to open his mind and heart to him. I ask my husband to stop doing the things that could take him from god, like video games, certain music. Anybody else experience something like this?

As a person who has anxiety, and nowhere near as bad as your husband's, let me answer from the point of view of the one suffering.

One of my biggest weapons against anxiety can be music and games. So trying to get him to give those up is counterproductive. And someone who continually pushes me to give up those weapons is actually part of the problem, not part of the solution. And may even come across as the dreaded "nagging wife".
You don't state where your husband's spiritual status is to start with, but if he's not a Christian games and music aren't really going to hold him back. And if he is, and games and music have that much of a negative effect then there's a deeper problem that needs to be dealt with. If a person's heart is right such things wouldn't sway a them, despite outdated religious perceptions.

I get caring about a person's spiritual well-being, but trying to pressure them into making choices or doing things You deem as right won't work. If he isn't doing it willingly then it won't be effective. Period. And even he he were to cave in and go along with you it may even cause resentment on his part.
If you want him to read or pray with you, make it an offer. "I'm going to go pray/read now, feel free to join me at any time if you're up to it" with a smile has a better chance of working than anything else.

If all they're doing is giving meds and sending him home it's time to ditch the therapist and find someone new. Or only stay for the meds (as they are Part of treatment) but perhaps find a counselor. Counselors are less trained but are more likely to have personal experience, and thus a better understanding that can't be gotten through books.

Anxiety typically has a core root. Meds are there to help lessen the symptoms so that they are less of a distraction from counseling. Which should be happening to find the root cause. Meds alone are like a bandaid on a broken arm. So it's no wonder he's not getting better with no counseling.
And often times anxiety goes together with other issues such as depression, which your husband almost definitely has as well.

Depression, also something I have, is a whole separate monster.

On top of what I've already suggested I would advise you to find some mental health forums and join. Many will be broken down into subsections for different afflictions. Find the anxiety area (and depression as well) and start reading.
Here you'll find people's first hand experiences of things similar to what your husband is going through to help you better understand. It's also common to find spouses of those who have these issues on there as well. And they may have insight and advice for you to learn from.
Also go learn about these issues from a clinical standpoint. Go to various sites and get more information. I found one of my biggest helps came from knowledge of what was going on inside me and why. I spent years learning about myself this way. And now I have less guilt and other weight's that my ignorance kept me locked up in.

As the spouse you have a tough road. I have a gf and I know how much work I can be because of anxiety and depression. Sometimes I feel it's not fair for her. That she'd be better off without me. I've made sure she knows and understands how bad it can be, and she's still around.
But she also listens to me and works at learning or remembering what to do, and not do. And she's done a fantastic job and it makes things easier for me, which is a big relief and also helps me appreciate her even more.
Oh. And she's a Christian, I'm not, so you can imagine that she has the same spiritual desires for me as you do for your husband. But she doesn't push. She understands I need to make my own decisions, even though I'm sure she'd rather drag me to God whether I like it or not 😂😂😂

My husband suffers from severe anxiety. He wakes up everyday throwing up because of how bad it is. Idk what to do for him, I ask him to pray with me or to read his bible and he won’t. I pray every single day for him and for god to open his mind and heart to him. I ask my husband to stop doing the things that could take him from god, like video games, certain music. Anybody else experience something like this?

My husband suffers from severe anxiety. He wakes up everyday throwing up because of how bad it is. Idk what to do for him, I ask him to pray with me or to read his bible and he won’t. I pray every single day for him and for god to open his mind and heart to him. I ask my husband to stop doing the things that could take him from god, like video games, certain music. Anybody else experience something like this?