What is the difference between Countenance and Mien?

I've never heard the word Mien before until today, and I am wondering how it might differ from the word Countenance.

From the OED:

Mien (noun)

A person's appearance or manner, especially as an indication of their character or mood.

‘he has a cautious, academic mien’

Countenance (noun)

A person's face or facial expression.

‘his impenetrable eyes and inscrutable countenance give little away’

While it seems that countenance is simply their facial expression, I can't think of a situation where a person has a facial expression for any other reason than indicating how they are feeling, since it is indeed an expression. Therefore it gives it to me the implied same definition of being an indication of their character or mood.

So I am left thinking the only difference could be appearance/manner vs. facial expression. So you could perhaps say:

His hat was tilted to obscure his face, giving him a distrustful mien.

But I sorta feel like you could use countenance for non-face related expressions, it feels like a countenance is a kind of 'read' you get on a person.

If you're outright, then I can feel it might not make sense, like this:

The scars and tattoos on his arms gave him an evil countenance.

Which I am not 100% sure is incorrect but it feels like it's heading that way.

Whereas,

His grin, along with the scars and tattoos on his arms gave him an evil countenance.

Yes, his grin works but the rest of the sentence isn't connected to countenance. It feels like it'd be the same as saying 'His raspy voice and scars and tattoos made him sound evil', like the scars and tattoos don't have an effect on the descriptive noun.

I am a bit puzzled. I also wonder if Mien is actually a word in common-usage. It isn't suggested as archaic but I have never heard of it before today.

Likewise with Mien, could you use it without an indication of their character or mood? It says especially, but it feels odd to say

The long yellow scarf and pink high boots gave him a colourful mien.

Or even

His mien was plain, he was of average height, weight, and was very unremarkable.

Merriam-Webster's Dictionary of Synonyms (1984) parks countenance and mien in two different clusters of words. Countenance appears in a group with visage, physiognomy, mug, and puss under the lead word face. Mien appears in a group with demeanor, deportment, port, and presence, under the lead word bearing. Here's what Merriam-Webster has to say about these two word groups and about the words of particular relevance in them:

Bearing, deportment, demeanor, mien, port, presence are comparable when they denote the way in which or the quality by which a person outwardly manifests his personality and breeding. Bearing is the most general of these words; it may apply reference to a person's mental attitude to others, his conduct in society, or his characteristic posture or way o holding himself ... Demeanor applies rather to one's attitude as shown in one's behavior in the presence of others ... Mien implies reference both to bearing and demeanor, often as suggestive of mood ...

...

Face, countenance, visage, physiognomy, mug, puss denote the front part of a human or, sometimes, animal head including the mouth, nose, eyes, forehead, and cheeks. ... Countenance applies especially to the face as it reveals mood, character, or changing emotions ... Especially in the phrases "to keep in countenance" (maintain one's composure) and "to put out of countenance" (cause one to lose one' composure) the term denotes the normal, composed facial expression of one free from mental distress. Sometimes the word is used in place of face when a formal term is desired ... Both face and countenance may be used in personifications when the outward aspect or appearance of anything is denoted ...

James Fernald, Funk & Wagnalls Standard Handbook of Synonyms, Antonyms & Prepositions (1947) doesn't cover countenance as a noun, but it discusses mien as part of a group of words that also includes appearance, bearing, behavior, carriage, demeanor, expression, fashion, look, manner, port, presence, sort, style, and way—all under the lead word air:

Air is that combination of qualities which makes the entire impression we receive in a person's presence; as, we say he has the air of a scholar, or the air of a villain. ... Mien is closely synonymous with air but less often used in a bad sense. We say a rakish air rather than a rakish mien. Mien may be used to express some prevailing feeling; as an indignant mien.

These two reference works thus seem to agree that mien has to do with the effect or impression of character that a person makes on a second person, whereas Merriam-Webster is clear that countenance is in the first instance a predominant physical expression of the face, and more generally a person's outward aspect. It follows that we might characterize Don Quixote as having a woeful countenance but a chivalrous mien.