What about phrasal verbs like sit down or go up as when you say, "the man goes up the mountain" or the imperative "Sit down", I wouldn't consider this phrasals as metaphors neither I would say you have to use the figurative sense in order to interpret their meaning.
I do understand that some of their meanings might be completely idiomatic but what about this more easy-to-understand meanings?
Should they be left out from the definition? by the way, are phrasal verbs always informal?
What is the definition of "phrasal verb"? From wiktionary:
(linguistics) A two-word verb, consisting of a verb and a "small" adverb or particle, that has an idiomatic meaning not easily predictable from the individual parts. In 'The police told the driver to pull over', 'pull over' is a phrasal verb.
By definition (according to that definition), they are "idiomatic".
Here is a list of 100 phrasal verbs: https://thefluentlife.com/content/100-most-common-phrasal-verbs-list-meaning/ . A few of them are not too difficult. "run into" "pick up" "pick out" "move out" , and more.
It seems the nature of phrasal verbs is that they jointly (the verb and the particle together) form a unit of meaning which is on par with a "word".
give up -> aufgeben (German for give up). "aufgeben" is one word. It has a meaning that's not necessarily what you guess from "auf" + "geben".
Consider the situation of a standard word.
"communication" -> "co(m)" means "with". "muni" goes back to proto-indo-european *mey- (“to exchange, swap”). So "communication" means to "exchange with others". But you couldn't necessarily guess the meaning of the whole word from the individual parts. You have to learn it. Likewise, you have to learn the meaning of "aufgeben", it can't be deduced. And also with "give up".
Should they be left out from the definition?
The criterion is not whether they are easy to understand, but rather if they function grammatically as phrasal verbs. If the meaning is literally identical to the meanings of the constituent parts though, perhaps it's something else. "the man goes up the mountain" -> a verb + a prepositional phrase. Not a phrasal verb.
are phrasal verbs always informal?
English is a hybrid of Proto-German, French, and Latin. The French and Latin versions of words and phrases are often seen as more sophisticated. The German versions of words and phrases are more common, basic, and informal. From this perspective, phrasal verbs are conversational and informal.
