Italian, I don't think you need to worry much about boredom. Your new child will have plenty to make sense of and deal with - new parents, new sibling, new home, new room, new toys&books, new rules… loss of previous carers… that's a lot to take on. You don't need extra diversions added on to that!
IF DC has been to toddler groups regularly, you could probably start going again pretty soon, in the sense of keeping some continuity to some part of their former weekly routine. But bear in mind that just because they are of an age to have experience with toddler groups, doesn't mean they have ever been; and that a toddler group may be a completely different experience for a vulnerable child, than it is for other children.
It would make sense to research the groups ahead of time. I take DS to a music session which is VERY small - 2-3 children. That kind of group would be relatively accessible I should think - I'd be able to talk to the group leader AND all the mums ahead of time if needed, too.
And remember, kids that age don't need much in order to be stimulated and not bored. A picnic in the garden can be a great adventure! IME (DS who is my BC is a preschooler) it's more likely that YOU get bored, than DC!
And you can keep boredom at bay easily by introducing some 'experiences' which your DC missed out on, as AllThings said. 'Feeding the ducks' will be an interesting feature of an outing for any pre-schooler, but can be an exciting highlight and main purpose of an outing if it is something they have never done before!
As you know, I'm not speaking from experience ;) but just trying to think ahead. One thing I'd keep in mind is, indeed, YOUR possible 'boredom' or rather, lack of structure to the days, which I personally would struggle with. With DS I found groups and classes a life-saver, as they provided a reason to leave the house, set times, a structure, and usually if you include the time to get ready, and to get home afterwards, even a short activity would have filled up a large chunk of the day. So, if you won't have any kind of 'scheduled' activities like that, at least initially, make sure you still have some sort of 'schedule'. And some (small, low key) plans that will get you both out of the house every day. (You might have 'forgotten', the amount of running around kids can do at this age!)
I assume that it might help your DC to have such a 'schedule', too. Not too many choices initially, no asking 'what would you like to do today?' but rather 'today we're going to the park in the morning, will pass by the post-office on the way back, have a small lunch at home, then stay at home and play until it is time to pick DD up from school.' So DC knows what to expect, IYSWIM?
Good luck with it all, it's very exciting!