When you talk about magical tinkering, it says this:
You then touch a Tiny nonmagical object as an action and give it one of the following magical properties of your choice:
The object sheds bright light in a 5-foot radius and dim light for an additional 5 feet.
Whenever tapped by a creature, the object emits a recorded message that can be heard up to 10 feet away. You utter the message when you bestow this property on the object, and the recording can be no more than 6 seconds long.
The object continuously emits your choice of an odor or a nonverbal sound (wind, waves, chirping, or the like). The chosen phenomenon is perceivable up to 10 feet away.
A static visual effect appears on one of the object’s surfaces. This effect can be a picture, up to 25 words of text, lines and shapes, or a mixture of these elements, as you like.
This ability specifies tiny items, and thus can not target normal weapons, so this is generally a moot point, but even if you have a tiny character with a tiny weapon, it still does not grant any weapon enhancing properties, and as such likely would not count as magical damage.
Now, when you talk about infusing an item, the description says this:
Whenever you finish a long rest, you can touch a non-magical object and imbue it with one of your artificer infusions, turning it into a magic item
Since it says that it turns the item into a magical item, so it deals magical damage
Hope this clears things up!