It means already 已经 in your sentence , I‘ve been sitting here for half an hour.
“都 ”is a time adverbs here, which been placed before time expression.
I have an easy way to identify when is 都 been use as time adverbs, you can add or replace ” already”已经 in the sentence, if it make sence, then it is a time adverbs.
eg: 我都(已经)在这儿坐了半个小时（time expression）了。
eg: 他都(已经) 8岁(time expression)了还要妈妈喂饭；
eg: 都（已经）8点（time expression）了你怎么还不去学校？
eg: 都（已经）11月（time expression）了，气温还是在30度。
Personally, I would recommend do not too struggle with Chinese grammar, as a native Chinese speaker I don't learn many grammars when I was in junior school, I just understand the situation, then next time I remember how to use it.