“Servant of God” just means that the person has an official sainthood cause open. The bishop or someone else with authority has to give permission to open the cause. An investigation is conducted and the evidence is sent to the Vatican (Congregation for Causes of the Saints). There’s no declaration on the person being in heaven yet.
After reviewing all the evidence, the Congregation can decide to name them “Venerable”, meaning they showed heroic virtue while on earth. Again this doesn’t say anything about the person being in heaven.
The next step, beatification/ naming someone “Blessed”, has been said to mean that it’s “worthy of belief” that the person is saved and in Heaven. Other definitions say it’s a declaration that the person is in Heaven.
It’s not an infallible statement because it comes from the Congregation for the Causes of the Saints and not from the Pope. The purpose of this step was supposed to be to allow local dioceses to publicly venerate one of their own who had not yet become a full saint because the process takes so long. At this stage, the person can have a feast day designated for specific locations, such as his home diocese or where his order was located, but not universal public veneration.
The last step, canonization/ naming someone “Saint”, means that they are certainly in Heaven and they can have a universal feast and parishes named after them. Canonization adds a person to the canon of saints and is declared by the Pope under papal infallibility.
Here is an article discussing the differences between beatification and canonization in more detail. I agree there is a lot of confusion between the two depending on what source you read. I personally think it’s pretty safe to believe if a person makes it all the way to beatification, they are in Heaven. But at that stage, since it’s not an infallible statement, Catholics aren’t bound to believe it.