Back when I did rescue I had a couple squirrels that had giardia. (among other things)
It usually infects animals/humans through contaminated water, direct contact, uncooked produce. In their inactive state, I can’t recall what it’s called, I believe they can live outside their host for several months. There are several species, many that can use both humans and other mammals as hosts, some are more specific.
Keep the area clean, if the puppy is using the restroom in your yard I would pick up any poops and dispose of them, so no one tracks in anything on their shoes. After handling the puppy wash your hands, especially when handling food items for your family or other animals. It’s shed through feces. If it were me I’d probably keep him from having access to hard to clean areas of the house, such as carpets and keep him from having direct contact with any other animals or small children who may accidentally stick their hands in their mouths before washing.
I was running a ferret rescue at the time and no humans or animals were infected other than the squirrels that had it. I have no idea what species of giardia it was or whether it could of passed to the rest of us, but we just used the same precautions as if it were.
Oh I just noticed it was last saturday that you got him, if he’s been on meds since then, he’s probably pretty safe. 7 days on meds is usually good. Though a little quarantine of any new animals is always good plan the first few weeks.
Grats on your new puppy, he’s adorable and sounds very well behaved for such a wee one!