You might want to take a look at what tesla describes the modes as:
Powerwall is configured to meet your home’s specific energy needs. Use the Tesla app to monitor and manage your solar system’s performance with features and control modes such as Backup Reserve, Self-Powered and Time-Based Control.
www.tesla.com
yes, self powered mode prioritizes using your powerwall power to power your home, till it drains your batteries down to your reserve. It makes no allowances for "peak TOU time" or anything else. In self powered mode, your home will run off your batteries until it either hits the reserve you set, or the PV system comes up and provides enough power to both run your home and fill your batteries.
Since self powered mode prioritizes "using as little grid as possible" that sounds like what you are describing you want, but since you also mentioned in other posts "Time of use, peak time 4-9pm" you would need to decide what you really want.
Its entirely possible for self powered mode to run your home off batteries during a cloudy morning (for example) and not "save some for peak time". Its my opinion that anyone using self powered mode that is on a TOU plan needs to be prepared to micromanage reserve settings, etc.
Based on things you have posted before, Its my opinion this would not be a good fit for what you want.... but it does exactly what you say you want in this thread, which is "use the grid as little as possible" (while ignoring completely any and all time of use settings etc).