Ideally it creates a CSV file and stores it on an SD card or something. I’ll even use on that requires an app as long as that app doesn’t make me create an account.
UPDATE:
I went with a Withings BP cuff. It doesn’t meet the above criteria at all, but I already had a Withings account from years ago before I was concerned about privacy so I wasn’t giving my info to someone who didn’t already have it.
https://github.com/openyou/libomron
This looks promising, it lets you collect data from Omron devices. It’s from a quick web search so idk any more about it.
One way this is better than manual logging is that it can run while you sleep. That is, you could have it take your BP once an hour all night or whatever. That’s done in hospitals all the time. It’s uncomfortable so I wouldn’t do it routinely, but it might be worthwhile if you suspect something might be up. Obviously, discuss it with your Dr too.