This week, next gen @element@mastodon.matrix.org client, Element-X, and @neochat@kde.social announced they are supporting #UnifiedPush. This makes 2 more @matrix@mastodon.matrix.org clients supporting it !
NeoChat the second Linux app officially supporting UnifiedPush, after @tokodon@kde.social
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You are forgiven. Element constantly runs a worker to check for new messages on the FOSS version (depending on your configuration), unlike PUSH which just sits idle and listen for new messages.
Some say "yes, by a lot". In my experience a 10 seconds fetch rate on apps costs only a few percentages of battery per charge if the fetch is reasonably sane. Checking 75 podcast feeds with thousands of episodes every 10 minutes isn't sane.
I have tested and got better battery on Lineage/Clean ROMs as compared with stock as well. I put it down to bloat and spyware constantly running in the background with elevated priviledge. 🤷♂️