How does the State Council direct the policies of the PBC? If it
doesn't, what are the executive authorities the State Council has over
the PBC aside appointing and removing deputy governors?
In a Western style political economy these would be important questions. In China, they really aren't.
The pervasive reality of the Chinese political-economy is that all material decisions are made by the Communist Party of China, and then the formal governmental institutions of China, including the State Council and the PBC, rubber stamp that decision (in China, that metaphor may even be literal, as signature stamps, rather than manual signatures, are used to approve many official document there).
There are examples of this happening in the past.
For example, the PBC absurdly inflated the inferred credit rating of state owned (and formerly state owned) enterprises with which it does business for political reasons, in a period in recent years when many of these businesses were actually financially stressed. In 2015:
Around 97% of existing yuan-denominated bonds hold ratings of double-A
to triple-A—the best a company can get.
according to Fiona Law at the Wall Street Journal. Thus, basically, the bond ratings of all publicly listed Chinese companies were wildly overrated. Meanwhile, a Chinese government agency, the China Securities Finance Corp (CSF), central bank-backed refinancing institution, was then "among top 10 shareholders of many listed-firms" as Chinese regulators have stepped in to prop up a collapsing stock market for political reasons according to China Daily.
The PBC enjoys some measure of independence because the Communist Party of China lacks the capacity or interest to treat most of what it does as a political matter in which it will chose to intervene. Most of what the PBC does looks like elaborate ministerial paper shuffling and accounting paperwork to the untrained eye.
But, on any matter in which the Communist Party of China's leadership feels that political intervention is merited, the Communist Party of China has the practical ability to secure the agreement from everyone who holds formal positions of power in the State Council and on the board of the PBC.
It isn't at all unprecedented in China for senior officials or executives who fail to literally "toe the party line" to be executed (either officially or clandestinely) with few, if any, formal legal proceedings in a matter of days or weeks, without any official acknowledgment that anything happened. As Forbes Magazine noted in a July 25, 2011 piece:
China Daily reported Friday that unnatural deaths have taken the lives
of 72 mainland billionaires over the past eight years. (Do the math.)
Which means that if you're one of China's 115 current billionaires, as
listed on the 2011 Forbes Billionaires List, you should be more than a
Mortality rate notwithstanding, what's more disturbing is how these
mega wealthy souls met their demise. According to China Daily, 15 were
murdered, 17 committed suicide, seven died from accidents and 19 died
from illness. Oh, yes, and 14 were executed.
China's list of billionaires also overlaps heavily (much more so than in the United States, for example) with its list of senior national government officials who are on the State Council and PBC Board. In the same vein, more than a hundred members of the Chinese national parliament have a net worth of more than $1 billion U.S. dollars as of 2017. By comparison, the U.S. doesn’t have a single billionaire in Congress.