Do multimeters take into account their own internal resistance?
Meters do not take into account lead resistance, unless they have a ‘nulling’ function like @jonk ‘s fancy meter, or it’s an even fancier 4-lead Kelvin type. This added lead resistance must be characterized prior to measurement and subtracted from the reading.
That said, lead resistance is only significant in the lowest ranges (20 ohm range or less). Lead resistance is normally about 0.2 ohms per lead typically.
More here: https://www.keysight.com/us/en/lib/resources/training-materials/tip-1-removing-errors-due-to-lead-resistance-372787.html