Is America (grammatically) a "constitutional federal republic" or a "federal constitutional republic"?

Grammarly says the adjective federal goes before constitutional, but I'm not sure what type of adjectives federal and constitutional are.

Here's what they said:

It appears that the modifiers in the noun phrase constitutional federal one are in the wrong order. Consider changing the word order.

Nouns can be modified by more than one adjective.  A specific order is followed for multiple adjectives.  Review the following list to determine the correct order.

Opinion — delicious, friendly, smart
Size — big, diminutive, gigantic
Age — antique, old, youthful
Shape — angular, flat, oval
Color — crimson, magenta, scarlet
Origin — American, eastern, polar
Material — cotton, iron, plastic

Various .gov sites say that America is a constitutional federal republic:

• The web site of the U.S. Embassy in Argentina.
• The CIA's World Factbook.

... and refer to other countries as constitutional federal republics:

• Brazil (in a Human Rights Report by the State Department).
• Nepal (in U.S. Relations With Nepal, also by the State Department).

The so-called rule is an attempt to develop a way for non-native speakers to figure out how to order multiple adjectives.

Google NGram results show that constitutional federal republic predominated until about the year 2000, after which federal is more often first.

https://books.google.com/ngrams/graph?content=constitutional+federal+republic%2Cfederal+constitutional+republic&year_start=1800&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Cconstitutional%20federal%20republic%3B%2Cc0%3B.t1%3B%2Cfederal%20constitutional%20republic%3B%2Cc0

The difference (and thus the choice) may depend on whether the author wishes to emphasize the federalism or the constitutionality of the government.

It seems to be a near-consensus among the regular contributors to this site that Grammarly and similar software are more confusing than helpful, and that it is best to simply ignore them. Even if one wanted to be more charitable to those who write and use such software, one would have to point out that it has never been (or should have never been) intended as a substitute for, but only as supplement to, learning about writing from human teachers. The software does not, and cannot, create authoritative rules for writing, but only get the users to think about, and apply, what they have learnt about writing elsewhere. Thus if such software generates a message that it appears that something is wrong, the crucial word there is appears. The point of the message is not that one must change what one has written, but that one should pause and think about whether one's wording is right, in light of what one knows about the matter. If one is confident that it is right, one should leave it as it is.

In this case, the relevant 'rules' would be the ones about the order of adjectives, but they, as has already been pointed out by Mr. Ashworth in a comment, do not imply anything about the particular adjectives in question, which do not involve colour, shape, etc. Moreover, these 'rules' are not really rules, but more in the nature of stylistic advice, and they should always yield to the established practices of experienced writers in the relevant field. Thus if you can point to reputable sources that use constitutional federal republic (as the question does) that is sufficient to justify your using the same wording in your writing, and ignoring the Grammarly's warning.