Bought an LFP battery+inverter set recently to replace an old dying lead acid based system. We need this kind of AC-DC roundtrip systems in India because of the unreliability of grid power (random power cuts, seconds/minutes to hours long).

Chinese cells (EVE etc) and BMSes (Daly etc) are easily available and all kinds of workshops build batteries at small to medium scale for all kinds of uses: electric auto rickshaws, power backup, sink for off-grid solar. Prices are $100-200/kWh for the battery depending on V, Ah and brand.

If you install a VPP battery in your house and the grid goes down, how much of that energy goes to you and how much is owned by the company?

I believe zero will leave your home. Most (all?) systems are required to stop back feeding if the grid reference goes down. Techs working on the poles want to know they will not get electrocuted.

They are going to assume all lines are live and ground them before working on them. But mistakes happen, so extra layers of safety are valuable.