Keep in mind that there are multiple text families within the Septuagint and multiple families of Greek translations beyond that, so unlike other texts, there really isn't one "official" Greek translation of the Hebrew Bible.
However, my recommended starting point for an openly available modern translation, one that is much better than the 19th century Brenton translation (but one that still has its own quirks) is the New English Translation of the Septuagint (NETS) which is available at: https://ccat.sas.upenn.edu/nets/edition/
If you happen to have a Logos subscription, the Lexham English Septuagint is also a good starting point.
Keep in mind that there are multiple text families within the Septuagint and multiple families of Greek translations beyond that, so unlike other texts, there really isn't one "official" Greek translation of the Hebrew Bible.
However, my recommended starting point for an openly available modern translation, one that is much better than the 19th century Brenton translation (but one that still has its own quirks) is the New English Translation of the Septuagint (NETS) which is available at: https://ccat.sas.upenn.edu/nets/edition/
If you happen to have a Logos subscription, the Lexham English Septuagint is also a good starting point.