Is there a good way to make vegetarian carbonara?
Do not look for all these functions in one off-the-shelf ingredient.

For the smoky taste and bacon texture, try various brands (there are differences in taste and texture) and cuts (as in, HOW you cut it) of smoked tofu. Dulse seaweed is also often recommended as a bacon substitute (but can taste too fishy).

Where hot saturated fat is needed, you will need to add that separately at the right time - or separately fry the abovementioned ingredients with excess butter/oil (getting some smoky flavor infusion) and add them with (or before) that excess oil. Butter or ghee/clarified butter (probably preferrable due to heat tolerance) are chemically closer (mostly saturated fat) to bacon fat than an oil.