will keeping my Honda Insight 2010 parked in the garage extend the life of the battery
high ambient temperatures are what kills a battery, so if the alternative to the garage is in 120º sun, then yes. Otherwise, no.
Agree with @BillRussell, age is also a factor. Most regular batteries have served their useful life after 5 years. If this is the original battery you got more than your moneys worth from it. Many McParts stores will check your battery and charging system for free. If you are concerned about your hybrid battery, check your owners manual. I have heard that 7 to 10 years is the useful life.
For some reason, Honda’s track record with hybrid battery life is nowhere near as good as Toyota’s enviable record.