Mostly, DMs control everything except the player characters: there are exceptions
Overall, I'd agree with the OP's position that a good DM will describe situations purely "external to the characters." A player has control of one aspect of the game: their character. As much as possible, they should retain autonomy in this control, including the actions, motivations, and emotions of their character.
The most "RAW" support for this position is the PHB's descriptions of the roles of players and DMs on page 6.
The DM describes the environment. The DM tells the players where their adventurers are and what’s around them, presenting the
basic scope of options that present themselves (how many doors lead
out of a room, what’s on a table, who’s in the tavern, and so on).
The players describe what they want to do...
The DM narrates the results of the adventurers’ actions. Describing the results often leads to another decision point, which
brings the flow of the game right back to step 1.
A DM might use emotional language as a shorthand to describe an environment or creature (a creature might be "terrifyingly ugly", or a house "unsettlingly quiet"), but such a description is still a description of the environment (things external to the character): not a description of a character's reaction. Also, it is worth noting that emotions are inexorably tied up in sentient motivation and decisions: what you feel in large part informs what you want. If the DM were to define the emotions of the player characters, it could reduce the players' role in step #2 (debatably, their main role in the game): deciding and describing what they want to do.
There are exceptions
That being said, in D&D (and some other systems as well) a character's emotional state can be a measurable game mechanic, that has a tactical implication in play. Take, for example, the "Frightened" condition in the PHB (p. 290):
- A frightened creature has disadvantage on ability
checks and attack rolls while the source of its fear is
within line of sight.
- The creature can’t willingly move closer to the source
of its fear.
Certain creatures in the game (like Ancient Dragons) can impose the Frightened condition on creatures that fail saving throws: their ability to do this is written into their stat-block, and this emotional reaction is not subject to player veto. A player cannot simply say "my character isn't Frightened of the Ancient Red Dragon because he's really brave." Being Frightened is a condition that confers specific game effects, is decided by dice rolls, and has starting and ending conditions that are well defined in RAW. As such, a DM can override a player's decision on whether or not their character is emotionally "Frightened". So RAW, DMs have some say in defining or setting the emotional state of player characters.
Similarly, the role of fear, madness, sorrow, or feelings of triumph may sometimes be up to DM discretion in specific situations where the rules define them, or in stories where these emotions will take center stage. The DMG gives rules (p. 266) for a "Fear" or "Horror" check, that applies to games where such emotions are a focus of the story (such as Ravenloft campaigns). And it's worth noting that even something as commonly used as Hit Points can be a measure of a character's mental state.
(PHB, p. 196) Hit points represent a combination of physical and mental durability, the will to live, and luck.
That said, in general, the division of labor is clear. In most cases, where RAW does not directly state otherwise (or the agreed upon nature of the story does not require otherwise), the players control the player characters, and the DM controls the rest of the world.