The answer is not a cut and dry one in your case. The troubleshooting is a process. You will need an understanding of a multiple light parallel circuit. You will also need a proximity type voltage tester and possibly a VOM.
Assuming the voltage feed starts at the switch (not always the case, but normal) you will need to verify input voltage at the line side of the switch with the switch in the off position. If you have voltage there, turn the switch on and verify voltage on the load side of the switch. At this point, a VOM is handy to test voltage across the hot and neutral and/or ground. If this looks good, proceed to the closest light fixture, and with the switch on, test the center hot tab in each fixture with the no-touch tester. In your case I would think you may not see any voltage based on your question. This could mean that you have an open neutral, an open hot, or at worse, a shorted hot to neutral/ground.
Since there are several possible reasons for your condition, it would take a lot of tutorial to explain every possible scenario. Assuming you do not see voltage at the fixtures, the basic technique for troubleshooting will be to start at the last known verified voltage point, then follow the wiring and check all connections in the junction boxes. Visually check the bulb sockets for broken or shorted metal tabs. This should be done with the power off at first, looking for obvious loose or disconnected wires, then with the power on using your voltage tester. Since this condition occurred after you adjusted the height of the sockets in the fixtures, I suspect tension on some wire may have pulled a wire out of a socket base or out of a wirenut in the j-box. Unfortunately, most can/pot lights have a built in j-box attached to the top of the fixture. This necessitates dropping the fixture down below the ceiling to access the j-box, or getting access from above. (attic).
Basically, you are following the circuit looking for an open or short, just like following a hose, looking for a water leak or stoppage.
This is not a hard job, but extreme caution must be taken when testing energized circuits. If you do not have good electrical skills, the proper test equipment, or a logical understanding of switched paralleled circuits, then this job is better left to a pro.
Maybe one of my buddies here on SE can add a good graphic showing this type of circuit and the test points. A simple line drawing showing the switch and junction points would be a great edit.
Sorry for the slow response, but when in the process of taking out the breakers to investigate the bus bar I figured out what was going on and it took me a few days to confirm it. The two bad breakers were in the same row of my sub panel, and it dawned on me that if one the lines from the main panel that feeds sub panel was bad, that could be causing my problem. So I tested the two breakers (tandem) in the main panel that were feeding my sub and sure enough one of them was putting out 25V. So I replaced the tandem breaker in the main panel and now everything is working agin.
Thank for your suggestion about the breakers being in the same row, which got me thinking about the problem in a different way.
Best Answer
Since this started after a high current event and you reset the breaker the problem is usually a weak connection.
Backstabs are the most common source of this problem. If you don’t have a meter or a receptacle tester you can troubleshoot by using a plug in lamp and working to the service panel.
Most homes are wired from the panel in a chain so I try to figure out what is not working on that circuit looking for the first working receptacle or switch.
This is where you find the problem the last working device or first non working device, most commonly a back stab or push in wire connector.
If you find the device turn the breaker off and pull it out and don’t see anything wrong and put it back in . then turn the power back on, if things start working that device will fail again and should be replaced or at a minimum wires moved to screw terminals.
If everything is still dead the problem also can be at a wire nut or a broken wire and the least common place is in the panel.
So you are looking for a loose or broken wire at a backstab /wirenut or screw. It is normally white or black.
Please turn off circuit breakers prior to working on circuits. There are non contact voltage testers that can alert you if there is power there test before touching! some for 5$, professional models usually run 15-20$ , add a receptacle / GFCI tester that can be purchased for 10$ or less should be tools every homeowner has to help them do basic electrical work safely and correctly.