https://en.wikipedia.org/wiki/IPA_vowel_chart_with_audio
German ö can be [
œ] or [
ø].
The chart tells you the position of the
blade of the tongue (i.e. it's not about the tip). The front of the mouth is to the left. The central mid position is the position of a completely relaxed tongue.
Compare with [
ʊ] in book or [
ɜ] in urgent. The former has the tongue in the back and high, while the latter is comfortably central and unrounded.
The 'roundedness' quality in the description of the vowel refers to the shape the lips make. The ö vowel is rounded. The lips are tense ('compressed'), which in some speakers may result in the sound being more central - that is, the tongue position may be closer to [
ɜ] in urgent - but the lips stay rounded.
Btw, if you want to realise [
ɜ] in isolation, you can try for the regular shwa [
ə] which is close enough. That's the first vowel in abroad, the last one in comma, or the vowel in the
reduced (weak, unstressed) 'have', 'of', or the article 'a'.