[Perseverando]

Armed militia in the Capitol rotunda.

No, those are not militia. They are the State National Guard units which have been federalized by POTUS.

States may have "militias." Fox example, Virginia has the Virginia Defense Force which is volunteer non paid "reserve" to the VA National Guard.

I am not sure about the semantics of other States' militias designations and Constitutional authorities.

[Dr. Franklin]

No, those are not militia. They are the State National Guard units which have been federalized by POTUS. States may have "militias." Fox example, Virginia has the Virginia Defense Force which is volunteer non paid "reserve" to the VA National Guard. I am not sure about the semantics of other States' militias designations and Constitutional authorities.

By statute, 10 U.S. Code § 246 - Militia: composition and classes:
(a)The militia of the United States consists of all able-bodied males at least 17 years of age and, except as provided in section 313 of title 32, under 45 years of age who are, or who have made a declaration of intention to become, citizens of the United States and of female citizens of the United States who are members of the National Guard.
(b)The classes of the militia are—
(1)the organized militia, which consists of the National Guard and the Naval Militia; and
(2)the unorganized militia, which consists of the members of the militia who are not members of the National Guard or the Naval Militia.
https://www.law.cornell.edu/uscode/text/10/246