This 'impeached/not impeached' argument is just semantics. It depends on what the definition of 'impeached' is. If we say that President Trump has been impeached as of the House vote, Ok, then so what? It makes no difference in any way, except maybe in terms of Democrat propaganda. But it does nothing to hinder or impede the President in any way at all. It is the same as nothing, except a word.
I know there are Liberals celebrating the idea, from there own words, 'We have put a stain on his name forever!', as if that is an accomplishment of some kind. By saying that, they are admitting that the entire impeachment ordeal was nothing more that an act of petulance and revenge. If to stain President Trump's name in history was the goal, then how does that achieve any practical immediate result?
The House repeatedly said that President Trump was an immediate threat to national security and world peace! What does tarnishing his name in history 20 or 50 years from now do to address the threat he poses today? The answer is it does nothing. Nothing at all. Gleefully calling him "impeached!", with no change in the form or function of his Presidency is vapor. It is a word with no meaning.
If we want to dive into deep technicalities, yes he was voted eligible for impeachment by the House. But without Senate involvement followed by any real-world consequences, it is the same as calling him a "doo-doo head" and nothing any more serious than that.