Indoor Biking - How would my device know the accuracy of my distance?

Several options there:

1. The bike transmits speed data over ANT+ (very rare)

2. Use a speed sensor (but difficult to attach to most indoor bikes, and speed might not correspond to speed displayed by bike).

3. After uploading to Garmin Connect, edit the activity, and manually set the distance to what your bike shows.

I use option 3, and so far I have been able to get some of the indoor bike badges.

If you sync to a power meter it will calculate distance based off your power

No, it won't. Bike power has no direct relation to speed, and besides the Garmin Instinct does not support power meters.

Ah ok well I literally just did an indoor cycling workout with my Fenix 6 synched to my Bluetooth smart trainer as a power sensor and it gave me distance and power. 

Not sure about the instincts capabilities though.

It's because the trainer calculates speed. It has nothing to do with power comming to the watch.

The only sensor I am connecting is power, not cadence, or “speed”. Garmin then calculates the power to a speed reading.

Most trainers that use power operate this way. As an example of what I mean, if you want to use zwift you are given the option of either a power metre or a speed sensor. You don’t need both.

But yea it’s irrelevant anyway because you are right an instinct can’t connect to a power metre.

So the only option would be a garmin speed sensor but whether or not that would work will probably depend on what exercise bike the op has.