The house was built in 1963. The cable is cloth covered Romex with ground. In 2005, the previous owner increased the service to 400 Amps and installed two Siemens panels (200 Amps each) and new Siemens breaker switches. One of the panels feeds a 100 Amp subpanel located in the garage. Outside of the house, a new panel and two master breaker switches (one breaker for each of the two 200 Amp panels) were also installed with a new meter. Ground wires run from the outside master breaker panel to a rod directly below it in the ground and a second wire runs inside and connects to the water supply line. The water supply line transitions from copper to PVC inside the basement, near the point of entry to the house - PVC runs to the street.

Questions:
Why aren’t the neutrals attached to the neutral bar? (Are the two inside 200 Amp panels effectively subpanels to the one outside master panel?)
Is connecting the ground wire to the copper water line correct given that the pipe transitions to PVC before heading outside to the street (the supply line is PVC)?

TIA

What you describe would be fine if this were the main panel. However, it seems like the main disconnect is not either of the Siemens panels are subpanels. You are right, the neutrals should be on their own bar electrically isolated in that panel from the ground.

As for the pipe, if the interior piping is copper (regardless of the external connections), it needs to be bonded. This isn't providing an additional ground (like connecting to the incoming metallic pipe would), but providing safety in case some live wire should come in contact with the interior piping that would engergize all your faucets ,etc...