Generally target schools in Singapore are pretty much the same elsewhere in APAC (your usual suspects like Oxbridge, HYP, Wharton and etc.) with the addition of
NUS Global MBA which is only prestigious in Singapore. You’ll do just fine with the LBS brand anywhere within APAC.
By PE, are you eyeing local-centric boutique firms like Quantedge and GGV or multinationals like Blackstone? The former is undergoing a hiring freeze atm and possible downsizing that results in analysts fronting many hats.
With your experience, you’ll be entering as a fresh MBA associate which would mean a drastic pay cut considering you spent some time in
MBB. Unfortunately, consultants doing a lateral jump to finance won’t be comp’d generously unlike someone in the STEM field.