The charging voltage of the two batteries is different, which may present a danger.
Ternary lithium batteries and lithium iron phosphate batteries have different voltages, so it is difficult to keep battery packs consistent when mixing and matching. The cell voltage of the ternary lithium battery is 3.6-4.3 V, and the cell voltage of the lithium iron phosphate battery is 3.4 V.
No, most Ordinary disposable batteries are alkaline. Rechargeable batteries usually contain nickel metal hydride, nickel cadmium, etc. Mixing them would cause chaos in their internal electric fields, with unpredictable consequences.
New and old batteries cannot be mixed. Rechargeable batteries have different voltages and internal resistances than regular batteries. Either way, don't mix them.