For an opamp configured as a unity-gain buffer, should its output DC level follow input DC level?
Ideally yes.
If you look closely, you may find it's some small but roughly constant voltage away from the input. This is known as the &quot;input offset voltage&quot; and can be up to 5 or 10mV in some opamps, 1mV in others, or microvolts in &quot;chopper stabilised&quot; opamps where DC accuracy really matters. (Check datasheets for the details)
Some opamps have offset trimming inputs which allow you to add a pot and trim that offset out.
If your amplifier is configured with gain, that input offset is multiplied by that gain, so many high gain amplifier circuits take care to reduce the gain to 1 at DC.