Yes, recently, Signal (with the addition of Stories) has consumed a significant amount of battery while on a call (I have seen a battery loss of 3-4% over a 25 minute call), texting, or just being open but not actively used. I did a lot of experimentation with Battery Saver and Signal (and other apps) to reduce battery consumption.
Even with Battery Saver enabled, if Signal's Battery is Optimized or Unrestricted and I "close" Signal, it moves from a foreground app to a background cached process, but it's still active, just not currently open. When I looked for open apps, I didn't find Signal, but it's still available and consuming battery as a background cached process. I found this by enabling Developer mode and looking at the "Running services".
- Settings > System > Developer options > Running services [these are foreground apps]
- Settings > System > Developer options > Running services > (triple dot) > Show cached processes [these are background apps]
Here's how I ensured Signal stopped consuming battery after I closed it:
- Set the phone to Battery Saver mode.
- Set Signal's battery mode to Restricted.
When I looked at "Running services", Signal is no longer present, and when I "Show cached processes", it's no longer present there, either. So Signal is no longer consuming any battery whatsoever.
Even though I set Signal to Restricted battery mode and the phone is in Battery Saver mode, I still received Signal texts and Signal phone calls. I'm still working with Battery Saver and Restricted battery to figure out if there are any "patterns" of behavior, such as lost or late notifications, missed calls, etc., with Signal, but so far, so good.
Battery Saver Mode
From what I have experienced, apart from the few advertised actions Battery Saver performs, it has had ZERO effect on caching apps, that is, allowing the apps to run in the background, until I set the Battery to Restricted and closed the app. Then, and only then, did the app stop consuming battery as a background (cached) process.