I'm averaging 3 hours a day outside of meetings. Mostly in 30 minute blocks.

Manager is wondering why I can't get work done...

Is the manager really that clueless?

Yes

30 minutes?

Luxury.

And once you have a block of time to use for productivity, all you can think about is "someone is going to interrupt me" which then interrupts your thoughts... then you manage to get past it and WHAM, someone interrupts you and you are like "God damn, I knew it, why did I even bother to make the effort to get focused". This is your signal to look for another company ;-)

Having 20+ meetings a week on average (28was the highest number) after five months I raised the concern about the project with all the managers and "important people" which didn't had any effects.

I left the company, best decision ever!