Based on my research into IPDA and algorithms, central banks, trading firms/hedge funds, and smaller banks use execution algos (EAs) for trading with different objectives. Small banks use EAs to split large parent orders into smaller child orders generally in one direction, buy or sell. These orders are executed separately over a period of time to either open or close positions.
Trading firms and hedge funds use opportunistic EAs to buy and sell to turn a profit.
Central banks use market making EAs to buy and sell in order to bring liquidity providers net positions back to or close as possible to neutral. (This sounds like equilibrium). Central banks use EAs cautiously and only during their main trading hours (ICT mentions hours of IPDA operation) and always under the supervision of people.
A key reason for using EAs is to access multiple liquidity pools in order to reduce market impact or footprint.
Much of this confirms ICT's concept of IPDA even if it is a made up name and not a single algorithm shared between banks.
This is similar to a parent child relationship between Central Bank algos and other smart money players, where smart money (including central banks) accumulate orders in consolidation before expanding price, then the central bank algo pulls them back to equilibrium like a parent calling their child that has strayed too far away. Then they rinse and repeat.
I am of the opinion that with the function of central bank algos to facilitate the provision of liquidity with minimal market impact, that liquidity itself is the determining factor in price delivery.