Full tile pool surface, heavy green algea in grout lines

I am looking to buy a home with a 20 year old tile bottom pool. The grout between the tile is green green green with algae. The pool is maintained weekly professionally but at this point I think the green grout is deep into the grout after 20 years.

I am wanting to drain the pool and clean the tile really well and see if I can restore the grout.

I am looking at renting a glass bead pressure cleaner to help restore the tile, and then using oxygen bleach to get deep into the grout, probably powder for of it sodium percarbonate to get it white again.

am I on the right track to restore this pool???

Hi, I cannot help you, as I don't know about such cleaning systems but it sounds rather drastic and destructive.
Personally, if it were me, I'd start by raising the chlorine level very high, to the super-shock levels indicated in our Best Guess Table and then brush daily with a wire brush designed for tile pools (they sell them). If, after a few days of this I saw no improvement, I'd go for more drastic means.

If the pool water tests OK (which means the Free Chlorine level is at the correct level for the stabilizer, aka CYA, level) and there is no other indication of algae, you may have to go to drain-and-refinish methods. But if shock levels of chlorine and wire brushing fixes it, you're done, and at far less cost.