5e: Artificer: Does infused magic item count against maximum number of infusions?

I would assume the answer is ‘no’ but I wanted to check.

It feels very odd to be able to replicate (up to) 4 magic items at level 2, but only ever be able to use two of them at a time at that level, because it just saves you a bit of money early on, Or, for example, if you replicate a bag of holding, you can only ever have one other infusion active.

I have seen a few people claim that the replicate magic item infusion does not count against the standard 2 max infusions (at level 2). Just that you are limited to having only 1 replica of your chosen magic item at any one time. The claim is that (TCOE p12) the reference to an ‘infusion ending on a bag of holding’ is only applied if you attempt to make a new bag of holding, but I wanted to ask what other’s thought

I like this second option better, as it means you can play more with your enhancement infusions and so that if you ever want to change your other infusions, you don’t have to constantly pick up every item that pops out of your bag of holding (since it would be the oldest infusion every other time, you would have to re-create the infusion and put everything back into the bag)