Summary - there can be only one ground - in your case the twin rods at your house.
The wires to the house will have a ground I assume you are using something like SER cable - 4 wires total - 2 hots, a neutral, and a ground wire. Pure copper - if you do aluminum you will need to upsize quite a bit and make sure where you connect is rated for AL at both ends.
The wire from the house is connected in your panel there and there is a neutral-ground bond screw there.
At the shed end you tie that ground wire to the equipment grounds for all the boxes, raceways, conduit, etc ....but no ground rod.
From the MPPT/AIO in the shed you run 3 wires out to the PV panels - the pos and neg and the EGC. The Equipment Ground Conductor is tied to the racking if metal, the panel frames, any combiner box ground. but no ground rod
NOTE - you can use one EGC for multiple sets of pv current carrying wires. Here is a link to the table from the NEC. The rules can get a little complicated but you size it for the expected current in case there is a fault. This means if you have just a pair of 10awg wires your max size would be 10awg. If you have 2 pairs of 10awg wires your max is still 10awg. This is because the max fault at a time is expected to be just one set of wires.
another note - at no point do you tie the PV current carrying wires or the battery wires to ground. You also don't connect pv negative to battery negative on your own. Non-isolated MPPT will do it for you and for the isolated MPPT you don't want to or you can damage it...
Generally you can go down one size and be ok, but consult the local AHJ and follow it ... usually they just say to use the NEC table.
Just because I can never find the chart for the EGC size when I need it, adding it to my answers
NEC Table 250.122 specifies the minimum sizes for equipment grounding conductors (EGCs) based on the rating of the overcurrent protection device (OCPD) safeguarding the circuit. Proper sizing of EGCs is crucial to ensure a low-impedance path for fault currents, facilitating the prompt operation of protective devices and enhancing safety.
**Using NEC Table 250.122:**
1. **Identify the OCPD Rating:** Determine the ampere rating or setting of the OCPD (e.g., circuit breaker or...
At the array you do not drive a separate ground rod.... If you are using metal racking then you can't help it and that is know in the NEC as an auxiliary ground and doesn't count.
At the array you will want a good DC SPD per set of PV cables. At the shed you will want a good DC SPD per set of PV cables. At the house and shed end of the AC wires you will want a good AC SPD.
For the wires between the shed and the array - they get sized based on expected current carried from the PV panels multiplied by 156% ... odd number... if your panels generate 10amp, the wire size must carry 10amp * 1.25 * 1.25 = 15.625amps -- this way no matter what short happens they wires don't get hot. If you put them in conduit with more than 3 current carrying wires you derate to 80% of what they will carry. The EGC is not a current carrying wire, but does count for fill when you figure your conduit size.