Op-amps are absolutely, 100% analog in every sense; there's no need to limit this assertion with the nonstandard adverb "technically". The term "analog" was invented in the first place specifically to describe circuits made out of op-amps rather than "digital" circuits. And, yes, you can totally balance the charge on your cells using op-amps and similar analog circuits. You will probably want some sharp PWM waveforms in the circuit, but PWM isn't all the way to digital.
I would question whether a PWM "technically" counts as digital... It is on and off, sure, but so is a mechanical power switch, which few would describe as digital. "Digital" is more when we get higher level values represented by multiple signals that are on or off (aka bits).
A mechanical power switch can certainly be digital; the Harvard Mark I digital computer was made entirely out of mechanical power switches, actuated by solenoids (so-called "relays"). It depends on how you use it—as you say, by combining multiple different bits, either simultaneously or serially.
I agree that a PWM signal is not really a digital signal, but it's kind of on the edge—for example, https://tinyurl.com/25y54mph is a simulation I designed of a completely analog PWM generator (a simulated LM324 op-amp, five transistors, 13 resistors, and a couple of caps), and several vendors offer better-designed versions of the same thing on an IC, but you can also get a perfectly adequate PWM signal out of a digital GPIO pin, and the PWM peripherals commonly included in microcontrollers are entirely digital.
