> support from India, including military protection

That protection is notional, and the expectation that China (their only other neighbour) is not really going to get aggressive about this peaceful tiny country, but then there’s Tibet as an example. So then why is it notional? If China were to get aggressive, we (India) will not be able to do jack about it because, hell, we couldn’t defend our own territorial claims and have been losing land to China, one outpost at a time. No, not only from the wars from decades ago, but also very recently — yeah, that means even after this omnipotent non-biological entity became our own version of the glorious leader.

Interesting parallel. Does this reliance limit Bhutan's sovereignty in practice? What's the trade-off?

Look what happened to Sikkim, when India annexed it. They have probably been reminded of that.