So I'm soon opening a restaurant and I'm obviously trying to rein in costs wherever I can. I had been thinking of foregoing a costly dishwasher and instead trying to upgrade the 3 stage dish washing system by adding a home sous vide cooker with bath as the sterilisation stage.

The health department will close you down. You need either a 3 compartment sink filled with detergent, rinse water and sanitizer, or an actual dishwasher with the right chemicals loaded. This isn't something you can just McGuyver together.

My thinking is that it'll reduce on energy and water bills

There's still no free lunch. Heating water to the required temperature requires the same energy regardless of if you use a water heater or a sous vide. Also, you'll kill your sous vide after a while. The home machines are not meant for for this.

I was wondering if anyone on this sub has seen anything similar used in a commercial environment?

I've seen all sorts of cobbled together stuff, but it only lasts until the first inspection or bankruptcy.

Any other advice on the right corners to cut would also be appreciated.

You need a dishwasher (machine) or a dishwasher (person). Until you get busy enough that it's impossible, if money is very tight, you can wash your own dishes, but you'll still need the sink. In fact, you'll need the sink even if you have a dishwasher.

What you spend money on depends on what you're cooking. If you're very focused, you can get by with almost nothing. For example, I know a pizza guy who ran for 40 years with an oven and a dough mixer. If you have a varied menu, you'll need a lot more.

The only thing I'll add is that used is a lot cheaper than new. If you can deal with the transportation, installation and maintenance and risk, you can often get a good deal.