unio

The -i- in the middle is not the country suffix. Esperanto builds country names with -i-: Anglo an Englishman gives Anglio England, Franco gives Francio, Ĉino gives Ĉinio. So unio invites the reading unu plus -io, the land of the one, which is a fine joke and not the word. Uni- is a borrowed Latin noun that arrived complete. The connection to unu is real at the level of Latin unus, but it is history rather than morphology: you cannot get from unu to unio by adding anything.

What Esperanto would build instead, and when to use it. Unuiĝo is a union formed by uniting, from unuiĝi, to become one: a merger, an amalgamation, the act and its result. Unuigo is the uniting of others, from unuigi. Unueco is unity as a quality. Unio is narrower than any of these and more institutional: a standing political or administrative body made of members, usually states. Eŭropa Unio is the obvious one, and Universala Esperanto-Asocio shows the other choice, asocio, which is what a voluntary organisation of individuals is normally called.

And it is not a trade union. That is sindikato, from the same French word English calls a syndicate, and Esperanto is firm about it: laborista sindikato, a workers' union, never unio. Unia is the adjective, uniano a member of a union. The Latin curiosity is worth keeping: unio also meant a single large pearl, which is why English onion and union are the same word, and why perlo thirteen ranks earlier in this chapter is a distant relative of this one.