I am about to start regrouting ( well not me actually)
My pool is 9 years old. It is 6m x3m x 1.5m with 10cm square tiles. Very similar to yours
Quoted Crocodile Premium or Weber grout.
Google for details
Cocodile in 20kg tubs (or powder form) at about B3000 per tub or B300 per packet
Either 2 or 3 tubs required. Quoted B10,000
Is this sensible enough ? Good luck
PS. This is for the grout only, not the ancilliaries