Ignition switch, that is the place the power to the starter originates. Turning the key all the way past “ON” to signal the starter to engage is unique to the ignition switch.
That is your starting point, check that you have power off that switch when you turn it past on to initiate the starter. If power is leaving the switch move to the fuse box and relays. That ignition switch is likely the problem due to the intermittent nature of what’s happening.

List price 49.00 part number 61 32 6 901 961, time to change (if you have never done it) 1.5 hours.