The rules for mixing potions is a variant rule that a DM has the option to use if they want. The optional rules state:
A character might drink one potion while still under the effects of another, or pour several potions into a single container. The strange ingredients used in creating potions
can result in unpredictable interactions. When a character mixes two potions together, you can roll on the Potion Miscibility table. If more than two are combined, roll again for each subsequent potion, combining the results.
This is a general rule for combining potions and does not specify any limitation with regard to where the potions come from or how they were made. In fact, the item doesn’t even have to be a “potion.” The last effect reads:
For example, a potion of healing might increase the drinker’s hit point maximum by 4, or oil of etherealness might permanently trap the user in the Ethereal Plane.
The implication here is that any magical brew (potions, elixirs, oils, etc) can be used. Therefore, any potion that the Artificer makes can be used in conjunction with the optional rule for mixing potions.
However, because the rule is optional, it is up to the DM to decide if the rule can be used so check with them.