Is there a term for "non-words" like "ha", "ugh", "huh", etc?

They are exclamations.

Exclamation:

a word that expresses sudden pain, surprise, anger, excitement, happiness, or other emotion:

"Ouch," "hey," and "wow" are exclamations.

(Cambridge Dictionary)

Usage:

Exclamations (also called interjections) often stand on their own, and in writing they are usually followed by an exclamation mark rather than a full stop:

• How wonderful!

• Ow! That hurt!

(Lexico)

Aren't they interjections?

According to the Wikipedia article, this category includes exclamations and hesitation markers as well.

Linguistically, they can be called vocables:

a sound that is used in a particular language, especially one that is not considered a word, for example a sound such as "la" used in music or an exclamation such as "huh"

(Cambridge Dictionary).

Another word which may be a little bit more recognizable outside of a linguistics context is vocalization/vocalisation, which means

a sound that is produced with the voice, or the act of producing sounds with the voice

(Cambridge Dictionary)

although that has some other, unwanted meanings, including the addition of vowels (e.g. to Hebrew text which is written without them), the calls of animals, or as a synonym for "speech" in general.

filler from Lexico

1.4 A word or sound filling a pause in an utterance or conversation (e.g. er, well, you know)

• “English speakers tend to fill pauses in our speech with ‘um’ and ‘er,’ but speakers of other languages use different filler sounds.”