Cells/packs used in these hobby applications typically lack an outer protective shell, and are of the pouch cell type. This makes them more susceptible to damage, but is done for primarily weight considerations likely. Typical notebook or phone batteries will be encased in some form of structure that protects them, and for smaller batteries, like in phones, can prevent the fire from exiting the enclosure to some extent.
Furthermore, these cells/packs are designed for shockingly high instantaneous discharge rates, which means that any accidental release in energy will be correspondingly fast and violent. It seems that protection of the battery is the charger/device's responsibility, so it's also easy to accidentally use batteries which have been overtemped/overdischarged/underdischarged/overcharged. (they also have much lower design cycle counts than typical electronics batteries). Typical electronics batteries have a chip in them that will disconnect the battery, sometimes permanently, should any of these conditions occur at some point in the battery's lifespan.
I would personally recommend against the storage or charging of such batteries indoors without measures to contain any potential fire. For what it's worth, discharging (and maintaining) the batteries at a low state of charge will also decrease the amount of energy available for combustion.
Many people store their batteries in an ammo box or "lipo safe" such as these to protect against fire: https://www.amazon.com/lipo-safe/s?k=lipo+safe
Also you have to store them in fire-proof LiPo bags and recharge them regularly to prevent voltage drops below 3V.
My experience is different.
My students absolutely abuse the cheapest lithium cells I can find - from eBay and salvaged from dead laptops.
They did some art on pieces of metal through EDM using dozens of 18650 cells. No problems.
They tested what would really happen to old devices subjected to a massive USB over-voltage by building the "Over-Volter 9000." No problems for the lithium cells.
They ran lithium cells in dead shorts, just to see what would happen. Maybe a touch of smoke.
The only 2 times I have ever seen lithium batteries melt down was:
(1) when I pulled an early lithium pack from a Sharp 486 laptop and ran my RC car off it. (Associated TQ-10) That melt down resembled a bubbling mud pit at Yellowstone National Park. That was the first lithium battery I had ever seen, and it was useless when the laptop died and early death.
(2) Another time I melted an 18650 cell by accidentally leaving it in a dead short as I wired a large battery pack.
In both cases, the combustion was mostly smoke and sparks, with little to no visible flame.
There's maaany stories & videos about Li-ions bursting into flames, but with very few exceptions they come down to:
* While being charged. Or even under extreme stress, like driving a nail through it, or hooking up to a car battery to watch it explode.
* In series configuration, with 1 of the cells being defective / much lower capacity than the others. Or using a mix of different cells / cells in different state of charge.
* Cheap / poor quality / fake cells.
* Physical damage.
* Connected to monitoring / protection circuitry, with that circuitry failing. Not to mention ridiculously cheap chargers that are basically constant voltage source without any kind of safety feature.
* Some history of abuse (under / overcharging , dropping from a height etc).
Loose, quality Li-ions just sitting on a shelf, bursting spontaneously into flames, is very very rare.