The burnout that you’re pointing out is a sign that it is work. People who play video games competitively often go through burnout:
https://www.cbsnews.com/news/esports-burnout-in-video-gaming...
So I think about it as this: if I regularly feel pressure to complete tasks that I don’t want to, then it is work. This covers activities that one is not paid to do and that others may call hobbies. For example, training for a marathon as an amateur.
I think it's work even if it's for fun. I'm like you, I'm a software dev and I code things as a hobby. I like exploring and making things happen and doing ctf type things. Even though it's fun, it still gets tiring and I have to take break.
Even with games, they're fun until they're not. Sometimes I get a few hours into a game and then just never finish because i can't force myself to enjoy the gameplay. I feel like at that point I would call it "work", but other games I can play up to 100 hours. I don't think i've ever stayed interested in a game longer than that.
But anyway, do something else to relieve the burnout, and then get back to it. Sometimes I just need a new project.
Work is tracing code written by others and implementing new features on top of that to someone else's specifications with input from non-developers on a deadline. More people involved = more work.
Even video games can be work. Think about being a video game QA person who needs to go through at test every edge case, even if they don’t like the game. Or someone trying to 100% a game, there are parts that will feel like work.
Leisure time can take many forms, and coding can be a fun hobby. However, if you do it at work and feel burned out on it, it could be helpful to have a hobby that gets you off the computer to create some more variety.
A barista likely doesn’t want to see a cup of coffee while they are off work, meanwhile there are tech worker who will turn making coffee into a hobby and they love it.
It’s not a question of if coding is work or not. It sounds more like coding is no longer providing you with enough variety and differentiation between work and leisure time. I know a lot of people who have hobbies that look like work, but they like it and it’s different enough from their day job that it’s enjoyable. Woodworking is a common example.