What this looks like to me is that your 24VAC transformer is not functioning properly.
C to G should be 24VAC - your reading is what looks like an induced voltage - where your wire just kind of runs along an AC wire somewhere and picks up an induced voltage from the other wire.
Since you have said you installed the other Thermostat with no C wire required and it does not work either lets just assume your C-wire scenario can be left out of the equation and the fact you read 2.8 VAC is not caused by a broke or loose C Wire.
Causes of a poor functioning transformer:
1: Transformer is bad.
2: Input Voltage is not correct.
3: Partial Short on Secondary side (This is actually similar to item 4.)
4: Hi Current Draw load on secondary.
So the question now is what is causing that situation.
Determine if you have good incoming voltage to the Transformer or Bad
First measure your Voltage at the TB where you have L1 / L2 on your diagram (from your link) - you should measure ~230VAC if this is under ~200VAC , using an Analog Volt Meter or a Digital Meter with Lo-Z measure from L1 to a Neutral (or Ground) and from L2 to a Neutral (or Ground) [The Ground Lug is fine) - your reading should be ~120VAC.
If your reading is less than 108VAC on either line you are browning out on one line, and there are two more tests I will need you to do in order to find the culprit.
Since I do not know you from Adam and do not know your skill level I will suggest an easy but unconventional method to identify the problem.
You probably have a Dryer in your home - you will need to unplug the dryer and test at the receptacle from L1 to Ground or Neutral and also from L2 to Ground or Neutral - your reading should be ~120VAC for each L1 and also L2 [230VAC between L1 & L2].
If the reading on L1 and L2 is low at the dryer you have an issue with power coming in to your home on which ever line [L1 or L2] that was low. Contact your Power Company.
If the reading at the dryer is fine and your power at the AC Transformer L1 and L2 one or the other are low - your incoming power to the home is correct - However your circuit breaker for your AC is probably defective and has a higher than normal resistance causing the voltage drop in one or the other line. Replace your Circuit breaker for the AC System. This could be any where from a 60 AMP breaker to a 100amp breaker.
If All of the above is fine and no issues:
Your secondary of the transformer might be either under a heavy load or partially shorted.
Determine if the Transformer is functioning.
Disconnect the Yellow Transformer wire from the RM contactor (per your diagram in the link).
Disconnect the 2nd Yellow Transformer wire from the Wire nut it goes to - again looking at your diagram provided.
With out shorting the yellow wires to anything - measure the voltage across these two yellow wires - Do not touch them with your fingers it is AC and you will get a shock or electrocuted. The voltage should be ~24VAC as per your diagram.
If the incoming voltage was fine and normal and the Transformer secondary voltage is low - for example ~22VAC the Transformer will need to be replaced. This Transformer is most likely a 10:1 probably 9.5:1 wound meaning divide the Incoming line voltage by the high number and that is what your secondary voltage should be. Sometimes a Xformer will mark the ratio on it.
If this measurement is ~23.5Vac and above the xformer is 'working'.
We need to load test it. Typically a xformer will fail on low voltage but can fail on load as well - if they fail under load they generally measure lower than rated voltages .
There are three possible load failures for a xformer :
1: You have a partial short or a heavy load draw that is in the circuit. (partial short in your case should be more likely unless you have added stuff and failed to upgrade to a heavier duty xformer).
2: Transformer fails under load because it is under rated for the load applied to it. Adding items to an AC system - for example other items that draw from the 24VAC off the xformer multiple t-stats, dehumidifiers etc etc .. this is a situation created by the additions and the xformer might only be rated at .5Amp or 1Amp. Upgrade the Transformer.
3: More rare scenario is to have proper voltage coming out, nothing partially shorted on the secondary and nothing wrong with the load. The transformer has overheated will fail on load , as I said this is more rare but possible.
Determine if there is a partial short on the secondary.
Connect your yellow wires back up - however disconnect in turn one circuit at a time that is connected to the yellow wires and see which one will cause your voltage to become normal ~24VAC - when that occurs you have found the circuit that is loading down the power of your secondary and you can troubleshoot that.