The fact that both devices became noticeably hotter and started using more battery after moving from version 26 to version 27 is important, especially since you did not have these issues on version 26.
Since the problem has continued through 27.0.1 and you have already found no obvious indexing or ongoing background activity, the next step is to see where that extra power is actually being used.
On the M5 MacBook Air, reproduce the problem using the same mid-level application and open Activity Monitor >>View ALL Process >> CPU and Energy.
CPU will show whether an application or macOS process is using significant processor resources, while Energy shows which processes are having the greatest effect on power consumption.
If the Mac is getting particularly warm, Window >> GPU History is also worth checking. (Apple Activity Monitor User Guide)
Also check System Settings >> Battery >> Battery Health and make sure the Mac has adequate ventilation and is being used within Apple's recommended operating conditions. (Apple Support)
On the iPhone 13, go to Settings >> Battery >> View All Battery Usage and look at the periods when the heating and battery drain occur.
App and System Activity can show which apps or system activities are using the battery and whether activity is occurring on screen or in the background.
Also check Settings >> Battery >> Battery Health & Charging. (Apple Support)
If the iPhone still reports an “Ongoing iOS Update” insight, allow that activity to finish.
Apple notes that tasks following a major update can temporarily affect battery life and temperature.
Since you have been experiencing the problem for some time, however, that alone would not explain persistent heating. (Apple Support)
For both devices, try to reproduce the same workload that previously ran normally on version 26 and compare the actual power usage rather than temperature alone. On the iPhone, also note whether it becomes hot during charging, during use, or both.
If the Mac computer continues to run unusually warm or lose battery quickly without an identifiable high-usage application or process,
Apple Diagnostics can check for certain hardware problems. A normal diagnostic result would not rule out a software-related issue. (Apple Support)
What you have established so far is that the change in battery consumption and temperature coincided with the move from version 26 to version 27.
The checks above should help narrow down whether the additional power use is coming from an application, process, system activity, operating condition, or hardware issue.
