While having a MacBook not going into sleep mode will lead to increased battery drain, such is not related to the issue of this Discussion, EarthBased.
However, thanks for confirming that you have been running Big Sur without trouble, until just recently, with «11.5.1».
(Of course, that, all the more, indicates that your issue is unrelated to the topic of this Discussion.)
The best recommendation, for you, is to start your own Discussion, so your issue(s) may be properly addressed. Or, you can contact Apple Support, directly, using the Get Support link, at the upper right of this page.