Good quality electrolytics can reform if powered up in a certain way and then used enough. I would think it's not so much about how often, but the process used on which kind of caps. I would say there might not be a simple solution for more complex situations. If there is a good study behind this for PCs, let me know! I've only seen a few cases.
There are some argument to be made that the power cycling put wear on components too. Again not an exact science. So if you're powering on more to try to save your caps, you might be shortening some other thing's life. So I don't know what harm really to let things sit for a long time. But it's hard to see if powering once a year will help. So either your using it regularly, or your most letting it sit. Not sure if any balance can be found!
In terms of many batteries, age and lack of use it pretty much kill them no matter what. Not sure that powering on will matter. You'll pretty much have to replace it eventually. The oldest RTC battery I've seen latest just short of 30 years. It was a high quality panasonic lithium, which are still made. So I bought another 😀 This type doesn't charge of course, so it won't matter turning it on.