I'm seeing that I get a red squiggle under the words asian and european. When I right-click either, it wants to capitalize the word. I wouldn't think a general type of thing gets capitalized, such as "evergreen tree", a type of tree, versus "Blue Spruce", a specific type. I would think I need to capitalize "Chinese" or "German" or "American", but not the broader types of "Asian" or "European".
All proper nouns need to be capitalized. I believe you are puzzled over whether "Asian" is a proper noun or not. I don't see why not. We need to define what a proper noun is:
A proper noun or proper name is a noun representing a unique entity (such as London, Jupiter, John Hunter, or Toyota), as distinguished from a common noun, which represents a class of entities (or nonunique instance[s] of that class)—for example, city, planet, person or corporation).
Now, I believe you think that "Asian" is too broad a noun to be called a proper noun, because it seems to represent a class of entities, that is, a group of various people, such as Spanish, French, etc.
Does that mean, however, that we shouldn't capitalize "Europe", but should just write it as "europe"? Of course not. "Europe" still refers to a specific place, a continent, and "Europeans" refer to a specific people, the people that come from Europe. And there's only one group of people that comes from Europe, the Europeans.
When using 'Asian' as an adjective, yes, it is capitalized based on the following logic:
"In general, an adjective is capitalized if its meaning is "pertaining to X", where X is some specific person, place, language, or organized group. Most capitalized adjectives are derived from proper nouns; for example, the proper adjective American is derived from the proper noun America."
In this case, Asian and European are proper adjectives, and are therefore capitalized.