Chains rarely brake from pure tension. Just about every (of the hundreds of busted chains I've seen) "failure" is due to some preexisting issue. maybe only preexisting for a few pedal strokes but not because the chain spontaneously came apart. Perhaps the most common reason is a shift some time before that wasn't done well and the too high twisting forces (that is why modern chains have peened over ends of the pins) managed to wedge a side plate partially or fully off the pin end. Then with only one end of the pin holding things together it only takes a high effort to bend the remaining side plate over and let the male end of the chain slip off the pin. Sometimes if the chain was installed with a connecting pin and if both ends of that pin weren't properly seated in the side plates the same prying off can happen. I have seen bent over teeth (again usually from jam shifting) damage chains but this is usually preceded by a lot of chain meshing complaints that are hard to ignore.

If you replace the chain check the cog teeth wear, a worn out cog will cause a new chain skip when under power.

You do shift with no pedal pressure all the time, don't you Andy