So this isn’t really possible tbh. I’ll try to explain the two challenges you face here, one is feasible but not supported the other is probably impossible. I mean I’m not going to definitively rule it out but extremely unlikely to happen seems like a fair assessment.
The first is that HA does not support importing historical data. An integration can only change the state of an entity right now. There is no way for an integration to change the history of an entity and say “this entity had this state from time X to time Y”. There’s a number of feature requests around this capability, particularly when it comes to historical energy data (here, here and here for example). It makes sense but its not possible currently.
The best an integration could do right now would be to rapidly change states for the queued messages. This ensures all state changes occurred but there’s nothing it can really do with the timestamp of those messages currently.
The second thing you’d need is for an integration to be able to import historical data and trigger state changes as if they occurred at that moment in time. Remember, each integration is totally independent. The energy meter integration has no idea about MQTT or anything like that. The only thing it is doing listening for is a state change event for an entity with id sensor.energy_red. Same with potentially many other things (templates for example).
So for this accumulator to be able to work correctly it would somehow need to receive and account for a backdated state change event. This is a major problem because to properly process a backdated state change event most integrations would need to see everything as it existed at that time. Think about a simple template like this for example:
{{ states('sensor.energy_red') | float + states('sensor.energy_blue') | float }}
If this template was used in a template sensor or a template trigger how would this work if it receives a state change event for sensor.energy_red in the past? It would also have to know the state of sensor.energy_blue at that moment in time as well. If it used the current value of the blue sensor but the past value of the red sensor then the result is nonsense.
Perhaps this second feature request could be somehow limited to just energy meter or integrations that only look at the value of a single entity. But if there’s any way an integration could look at the state of multiple entities there’s really no way to handle a backdated state change event. Recreating the entire state machine at that moment in time is just not feasible.