As above. I'm looking at the OPA548.
The max. output current is 3 A, but reading the datasheet, I'm unsure if that's from the +/- Vin or the +/- Vsupply.
The output current is only ever supplied from the Vsupply pins.
Any input current that flows is tiny, and unrelated to the output. The nA-level bias currents that flow eventually end up in the supply rails. Input current flowing through ESD diodes also flows to one or the other power rail.
The output current limits affect the output only, according to the table in the datasheet:
The inputs are unaffected under normal conditions. It is assumed that your power supply can provide any current the op-amp might call for. If not, and the power supply(s) collapse, then you could conceivably have issues since the input voltage limits are related to the supply voltages.
Aside from the current limits you can program, there are also SOA and thermal limits that should be observed, and are described in the datasheet.
V+ and V- are power supplies of the Op-amp. They define the transfer function which determines what positive or negative levels of output voltage swings the Op-amp can have. If you reduce these voltages which may be already rated at less than 3A,you reduce the voltage swing and you reduce power supplied to the load.If you use a power supply,you have to make sure it can deliver the current and voltage the load requires.
First thing to know is the power requirement of the load and its voltage and current swing requirements. Then you design the power supplies V+and V-. The input voltage source sometimes cannot drive the load of the Op-amp on its own if it's too low. Op-amp is just a voltage amplifier of input Voltage source. Current to the load at output is coming from power supplies V+ and V-.