Let me try to clean up my understanding of the situation, I'll convert to US Dollars to eliminate some of the "noise"
Hero has a $285 stack. BB just rebought for $900. Late position new player holds $400ish.
Blinds are $1/$2. LP raises to $7. Hero 3-bets to $21 from the small blind. and both noted players call. That leads (somehow) to a preflop pot of $67, Hero's stack is now $264 ( Hero is the effective stack) and a SPR of ~4.
Did I get that right?
Observations:
Hero's table image is meaningful vs the BB but the new guy might not know this.
I have doubts about the wisdom of three betting jacks from the small blind given the stack sizes. This is villain dependent though, Hero might be properly planning to outplay the villains.
I have serious doubts about the skills of the BB and his "TAG" description. There aren't many hands I'd be flatting a 3-bet in the big blind, maybe BB is trapping with a bigger monster or AK?
Hero got lucky on the flop - well we hope Hero got lucky anyway.
So Hero needs to bet. Lets try $60 into a $67 to try and compensate for Hero's bad position. The plan is to shove $204 into a $187 heads-up pot or $204 into a $247 three-way pot on a brick.
Hero should consider a bet/fold line vs the BB and a bet/call line vs the LP villain on the flop.
If Hero feels uncomfortable in this spot even with a lucky flop (I would), then he should take this hand as a primer into position and SPR strategies. Not to say that Hero can't win a nice pot, just that bad position plus the higher SPR might suggest a safer / more profitable line vs many types of villains.