3 refers to the Monday that comes for the third time in the given month. All months have 3 because all months have at least 21 days. Likewise, there is no month that has 6. Note that 3 in Japanese never refers to the third day of a month in the first place.
Also note that your definition #2, "Monday that is in the third week", is probably inaccurate. For example, The 3 of September 2020 is the 21th (see the calendar below), but I think many people think "Monday that is in the third week" refers to the 14th.
![enter image description here](