The whole "partial discharges are bad" thing dates way back to the old days of timer-based NiCd chargers. Back then, chargers were dumb - they terminated the charge cycle based solely on a timer, and not based on detecting a full charge. The infamous "memory effect" wasn't actually the thing at play in most cases there - it's actually extremely difficult to reproduce outside of a lab. The problem was simple overcharging due to dumb timed chargers. As far as users were concerned, the symptoms were the same as "memory effect" so the myth stuck.
In general, partial discharges/recharges of a lithium-ion are far less stressful to it than a full discharge/recharge. However - li-ion/li-po batteries tend to lose capacity more rapidly if they are routinely kept at a high state of charge. Lithium batteries are "happiest" when they hover around 50% state of charge. (This is one of the reasons Teslas default to only charging up to around 80% unless you specifically "top it off")
Lead-acids like most non-EV car batteries are quite different beasts - they are happiest when fully charged, and will lose capacity RAPIDLY to sulfation if let to sit when partially discharged.