I know that my dh kinda found that there wasn't much he felt he could do for bub? I just got so good at doing everything, and I think he kinda felt on the outer a bit.

Things that helped were giving dh a job to do with bub and then commenting on how well he did - LOTS of encouragement and praise, and bite your tongue when he does it all wrong and different, and say 'aww she cries when I try it too, but I think she cries less for you'. Or something. Dh was just so unconfident, and I would undo it all with my impatience when I said 'here, just give him to me'.
It will take time for him to feel comfortable with any job, and you just need to keep being positive and saying 'you're such a great dad', you're doing so well.

Think about it - in those early days, bub wants mum, mum has boob, mum has the voice bub has heard their whole life, mum has 'the touch'. Dad just doesn't!

I've found as bub gets older, and dh can interact with him more, things are much better, now either of us can do the job - feed, bathe, play, settle.
Bathtime is a popular one for dads with new babies, cos it's one of the few things that mum doesn't need to be there for. Nappy changes too. Oh, Jodie has a good idea with a bottle feed of expressed milk too, if she takes a bottle. ETA: And Sherie has a good idea with playtimes.

Also perhaps, a chat - either with you or someone else. Despite his lack of confidence, he needs to work at this.

I don't know if confidence is the problem, but it sounds a bit like my dh was, and many new dads are like that - and I can't tell you enough how much just laying the praise and encouragement on thick and BITING my tongue helped his confidence. If you need to leave the room to keep quiet, then do so. If you stay, encourage encourage - and if you MUST give a hint, give it in a way that's not 'I know best' - try something like 'oh it took me aaaaages to figure out that I needed to hold him tighter', or whatever.

Oh, and hugs , I remember how hard it was watching dh seemingly not care, or not be interested. It's hard. But once I figured out that much of it was a confidence thing (though some of it just does naturally get better as bub gets older and can interact more), and I knew to encourage, things got so much better.

All the best.