Translation:Last year I was not happy, this year I am.
In English, we could also say this as "Last year I was not happy, this year I am.", implying not "this year I exist" but "this year I am happy".
Can you make a similar abbreviation in Hungarian, e.g. Tavaly nem voltam boldog, idén vagyok.? Or perhaps Tavaly nem voltam boldog, idén igen.?
Yes, we can do it. Your second example is perfect. The first one requires a little change: Tavaly nem voltam boldog, idén az vagyok. The ,,az'' refers to the ,,boldog''.
I kind of get the az variant. But how is igen fitting here? It usually means yes or something like nagyon?
Igen means 'yes, I am' here, as an opposite to nem voltam in the first part of the sentence.
When you have a yes/no question in english, you can answer 'Yes, I do' or 'No, i don't'. Hungarian simply say Igen or nem. That's how this 'igen' gets there: answering if I am happy this year.
Is this sort of similar to nem x,hanem y sentences? "hanem y" being just "igen"?
Does it require nem in the first part? I am not entirely sure what has to be in a statement to have "yes" in it, while it would not show in a translation.
Any chance of some short examples for this use?
I would assume the other way around should also be possible: Tavaly voltam boldog, iden nem.
Is the word order constrained by the implicit comparison or not, i.e. would either or both of:
tavaly nem boldog voltam, idén boldog vagyok. tavaly nem voltam boldog, idén vagyok boldog.
be also grammatically correct?
To make a general statement about your emotional state, you would say 'Boldog vagyok' or 'nem vagyok boldog.' Changing this word order would change the emphasis.
1, tavaly nem boldog voltam, idén boldog vagyok. - Grammatically, it is correct, but sounds unnatural to me. I would say it to imply that I was feeling something else (sadness, jealousy, etc.), but wouldn't like to clarify. If you were my best friend, you would be nodding along, knowing my history with my cheating ex, but no one else would be any wiser about my personal life.
2, tavaly nem voltam boldog, idén vagyok boldog. - This is correct grammatically too, although it implies that something significant has happened since last year, which makes me happier than ever. In this context, you shouldn't necessarily take the first part seriously, it sounds like the past happiness seems nothing compared to the present happiness.