inverter's grey plug voltage

I'm not sure I see a gray plug in your photo. I see the round two-conductor connection at the left, which supplies the A/C compressor, if I remember correctly, and the black multi-pin connectors at the right.

What those are for is ... everything else: the 12 volt power supplying the internal circuitry; communication lines and status indicators so the inverter can be controlled and monitored by the car's power management control ECU, connections to the resolvers of MG1 and MG2, and so on.

So a simple "what for is it and what is highest amps" question is probably too simple. Perhaps if you said a little more about your project, your purpose would be more clear. You can find details of what circuits are included there, and what they are for, in the wiring diagram.

 

If you look at this page on the PriusChat wiki:

Toyota Service Information and Where To Find It | PriusChat

you will see a link for a Wire Harness Repair manual. It's an attachment there, you can download it.

It will show how to correctly carry out those kinds of repairs.

The part numbers of the repair terminals you will need can be found in the Electrical Wiring Diagram, also described on that wiki page. In many parts of the world, it is available online, for some small fee. I do not know the details for Israel.

 

If you are talking about this round plug on the left hand side of the picture, I believe this plug has the same voltage compared to the round plug (the one to the passenger side of the 3 plugs in the back). If you bother to take a look inside the inverter after taking all 4 plugs off, you'll find that this plug is actually connected to the other round plug inside the inverter. Both wires go to the positive lead of the hybrid battery.