Tldr :
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Early days of Lithium batteries (2000s) were kind of a mess. You're fine now, thanks to lots of regulations and product maturity.
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Batteries can still catch on fire in case they're smashed, pierced, wet, or exposed to extreme heat (+60C). Have your battery replaced if it was damaged in an accident.
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Batteries are expensive. Don't be tempted to buy cheaper options, and don't trust Chinese knockoffs. If the price is too good to be true, it's probably counterfeit and some of the security checks probably haven't been implemented to save on production costs.
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Some micro mobility solutions (think urban e-scooters and bikes) were the first to try to save costs and reduce the quality/security of their batteries. Mostly solved by now, but more regulation is happening.
Apply all these to not only the batteries but also their chargers and you'll be completely safe ๐