Light going out when furnace or refrigerator kick off

I have recently added a new circuit in my basement that includes a couple of wall switches connected to can lights in the ceiling and a 4 plug outlet. One of the can lights has a habit of going out, even though the wall switch is still in the on position. When I turn the switch off and back on, the light comes back on just fine.

After some observation I have noticed 2 events that trigger the light to turn off. It happens when the condenser on a mini-fridge shuts off (not on) and also happens when the furnace kicks off (not on). The mini fridge is on the same circuit with the affected light, but the furnace is not. The breaker is not being thrown and nothing but this light seems to be affected.

It is a cheapo LED light, so not so easy to just replace a bulb. I assume I could find one online if that’s what I need to do, but I was hoping for some troubleshooting suggestions first.

Any idea what could be causing this?

edit: To clarify, it doesn’t happen every time the appliances kick off, but a few times a day.