Battery Issues
Although apps that log workouts or sleep can run constantly in the background and might read the users heart rate or location data in realtime, which causes additional battery use, this is not the case with Training Today, because the app is not built in this way.
When in the background Training Today it is not performing any logging and only checks for new HRV measurements once in 30 minutes and then updates the complications if necessary.
Apple limits the number of complication updates to 50 per day and we only get a few seconds of execution time to complete the queries and complication updates.
So it's highly unlikely that Training Today complications or the app will cause any additional battery loss since the large majority of the time there is no activity from the app at all.
Rest assured that Training Today is not likely to be the culprit of any increased battery use on your Apple Watch.