Hmm. I do wonder if there is the possibility to over think this.
Totally understand this and many people think 'it works so everything is all right' (not that you were saying that). However, your trailer is a special case electrically. It contains power production, power use and a means to make you and the ground around it wet in situations where you or others are likely to be wearing little (without going back I cannot remember if you have installed a shower but you could if you wanted to, in any case, you could use it for washing). Wet body in contact with the ground or a rubber mat that is wet to the ground means a more conductive body. The RCD protects you from faults to earth causing the trailer to become live by disconnecting L+N. You know this which is why you've done the job right. The only thing you don't know is that the RCD will disconnect BEFORE you are hurt. That is why it needs testing for disconnection time.
It's a trailer. Not a nuclear power station
Doesn't matter. Electricity doesn't care where it came from, under ideal conditions at anything above 25v AC it can kill a wet body anywhere and above 50v a dry body. It only takes 40mA to cause fibrillation.
I have one of those plug in testers by the way and it says all is good.
That tester tells you (depending on what one you have) that the supply is wired correctly and with the better model that the supply is earthed well enough for your on board protection to trip. It doesn't tell you that your RCD will work out of the box or that anything else is correct. You need to use it everywhere you plug your trailer in to make sure the supply is correctly wired and alter your adapters/connections accordingly to make it right. If you only plan to use the shore power at home then as long as that supply is ok all should be fine*. See below.
No desire to die here but it's just a 3 pin socket for a hair drier you know.
If you only intend to use one item at a time then no earth stake is deemed necessary for power from the inverter.
Let's say you only intend using shore power at home to charge the batteries (once you have your charger installed) then the setup you have is likely to be fine*.
* In the UK we have a wonderful system by which the electrical distributor (DNO or Electricity board depending on what you know it as) can use cables with one less core to them. This is called Protective Multiple Earthing (sounds good and safe doesn't it) or PME for short. You will know if you have it if your house has a label or takes its earth cable out the side of the big fuse on the end of the supply cable (if not then there is less danger and you will see this by the earth appearing as a clamp around the lead sheath of the cable). This PME cable combines the neutral and the earth in one conductor. This is electrically good when everything is connected as it should be but if the neutral becomes disconnected outside the property (which it can do more often than you may think) then the earthed metalwork and everything that is earthed becomes live. [emoji33] This is OK all the time everything within reach is connected to that same earth and nothing else can be touched so YOU cannot complete the circuit (like the bird on the high voltage wire doesn't get a shock as both feet are at 400kV). This is why those annoying earth wires are connected to the gas pipe and the water, taps etc.
The problem comes with any earthed metal that is outside the house where you could be in contact with the soil (True earth) where you could complete that earth return path such as from an outside tap or your trailer metalwork to the ground. No amount of RCDs will protect you from this as this can happen with your RCDs or main switch in the off position.
Assuming that your house has a correctly wired, up to date, correctly functioning electrical installation, all protection should be provided within that installation.
Back to your trailer being a special case, it can be plugged into anywhere in any country that may not be up to the same standards as your house installation (including a less than adequate one in the UK). The safest way is then to provide your own earth (stake) and make sure your trailer is far enough away from other metalwork that it cannot be touched simultaneously. Greater than arms length, 2m or more.
Long story short, your correctly working RCD will protect you from earth faults occurring within your trailer whether or not you have an earth wire connected (better if one is there). You need protection against introducing a dangerous voltage down the earth wire. This is where you need to make a judgement as to what to do which may well be not to use the supply, though you could put down an earthed mat or stake to make what you stand on and touch the same voltage.
Overthinking? I like to think of it as necessary thinking that has been done for you (and others). In this case (and daily in my work) I prefer to overthink than under think. I think that's good thinking, don't you think? [emoji4]