I wish my SO would take an interest in tho stuff (mostly because it would make it easier for me). I think it’s great that your husband wants to take action if he feels he needs to.
I think it’s fine if you both take on different approaches. I know I’ve had to figure out what works for me - you probably have too - and he probably wants to do the same for himself as well.
If you’re seeing results and he’s not, odds are he’ll ask you for tips, which will likely be much better received than if offered unsolicited.
I’d say that if you’re trying to be more supportive, look at the ways he’s supported you and try to emulate that. Let him do his thing, praise his successes and be a sounding board for his frustrations.

Me! DH and I have a history of exercising and getting healthy together, when we first moved in together we were in the best shape of our lives. He introduced me to lifting and we both watched our macros and logged our meals. As always, life happened, I lost my job and thus our gym memberships, we moved in with his parents and ate like them.

FF to now, 3 kids later, I decided to get healthy again. He wanted to with me, but had to have minor surgery so he put off starting. After he healed, he joined a gym. He went for a couple months, but his interest has waned. We did meal prep together, but then life happened and he lost his job. Our grocery shopping has changed. He quit logging his food and started spacing out his gym visits. I quit too, but only for a couple of weeks. I've fought tooth and nail to get myself back into the food logging habit.

For me, I'd rather just be doing it myself. I want him to eat healthier and lose weight, he needs to lose weight. But because our motivation levels do not match right now, it is frustrating. I feel like I'm putting out an A effort and he's in the same class but putting in C work, you know? It's okay that he isn't as into it as me, and I try not to frustrate him. I know he's job searching and going through a lot. But it doesn't make it frustrate me less.