While this is not a DIY post, it is an example of why we don't answer DIY questions. When considering a particular question we don't know all the related questions which aren't being asked.
If you consider only the garage door opener, then the cost of powering that opener is in the noise compared to the cost of an upgrade for a house panel or the cost of running separate tenants power to the garage.
But you have to ask 'what else does the code require' when power is brought to the garage. The cost to run the opener is nothing compared to the costs of other things which might get plugged in to that outlet, or other required outlets.
Separately: the energy use of moving the door is probably small compared to the control circuit which draws less power but runs continuously. For every watt of standby power the unit consumes, you have 9kWh per year of consumption. 10W of standby, 20 cents per kWh, and you are at $1.50/month simply to have the opener plugged in.
The OP might consider some sort of solar/battery powered opener, specially to avoid all the costs associated with bringing mains power to run the garage door.