I would argue that Beijing didn't anticipate the resolve of the protestors, but they would certainly know about and endorse Lam's backdown.
China is happy to play the long game - they apply pressure to HK to bring them inline with China, people protest, they back of a little, but not all the way. They wait ... then apply pressure again. The idea is that by 2047 when the 'one country, two systems' arrangement expires, HK will fully accept the China way of life. Lam backing down is an easy way to defuse the situation for now and they can try again later.
I expect to see this cycle of peace, then protest, then peace again continue for years - each time, HK will lose a few more rights they used to have.
China is happy to play the long game - they apply pressure to HK to bring them inline with China, people protest, they back of a little, but not all the way. They wait ... then apply pressure again. The idea is that by 2047 when the 'one country, two systems' arrangement expires, HK will fully accept the China way of life. Lam backing down is an easy way to defuse the situation for now and they can try again later.
I expect to see this cycle of peace, then protest, then peace again continue for years - each time, HK will lose a few more rights they used to have.