This will be two questions in one.
1: Is "italic" reserved only for styles that change base shape of glyphs (a/g)? I have a font which is optically corrected, but it's still just a slanted version – all glyphs look the same. I have a single-story /a as a stylistic alternate for both upright and slanted versions though.

2. Which Cyrillic letters *have* to be italicized? I've seen all kinds of variants, /de seems to be done the most often. Bulgarian alternates use the cursive form by default even in upright styles.
Comments
Most of your customers probably won't really care. Traditionally, Italic would have more alterations than you show, but on the other hand 'oblique' might be a foreign term to some. In short: I wouldn't worry about it too much.
The Bulgarian г looks a bit unbalanced/more slanted to my eye, as oval italics tend to do. And the Cyrillic a should be the same as the Latin one. There is a Macedonian г - check Wiki again.
I agree with Jasper de Waard that most customers do not care. I include all possible versions when I have to, personally.
I feel like there are some width issues with your font (in both styles), the n looks very little compared to e, o...
ч tends to be a problematic letter across italics and bolds, keep that in mind, it needs more treatment than a simple slant.
PS In certain designs there can be included a macron above m and under ш to differentiate them from ж and one another. Certain designs. The macron has no sound value and is simply a prolonged element.