Riese Muller with Bosch performance CX not engaging immediately

Since your bike has a derailleur and you recently changed the chain, I am guessing that the cassette is worn out as well, especially in some gears (it may be the case if you often keep the lower gears because the motor bail you out of steep hill & co, when you pedal at a much lower cadence, too slow if you did not have a motor, but you can keep going because the motor is there to support you).

I read what you describe as the chain not engaging immediately on (some worn-out teeth of) the cassette, probably because of the additional torque released by the motor post-firmware. So teh chain slips and to you it feels like the motor did not engage. However, this is a mechanical issue of the cassette, not of the motor, teh motor feels the chain gliding smoothly so it does not apply any torque ... but the issue is the chain not hanging on the rear gears.

It is a well known musical phenomena of bikes without motor: you stop, you get ready to start, you prepare your strong side to have the pedal in the upper position, you push hard with that leg, suddenly the chain slips, the pedal rotates quickly, the foot belonging to the strong leg lowers suddenly and your crotch hits the top tube, music and religious invocations start filling the air.

In short: you should go to the bike shop that changed the chain and ask why they didn't check the rear cassette.

It’s definitely just your freehub’s slow engagement. The old firmware might have had a smoother introduction of motor power at the expense of responsiveness. The new one might be snappier, which means you’ll feel the dead space more. This problem will manifest itself more in the lower gears because you have to pedal more to rotate the rear wheel the same amount.

Edit: Thanks to Affe, I’ve learned that I got it backwards. The new update is in fact more gradual, so I presume there’s more of a delay before the motor fully kicks in. Your legs will be the primary power source until then, so you’ll feel the freehub delay more clearly.

Depending on what rear hub you have, you may or may not be able to add more pawls for a faster engagement. If your hub is incompatible, you’ll need a fancier one.

The 2020 Bosch performance CX firmware update does change the algorithms for adaptive support in addition to increasing low-cadence torque. It intentionally 'ramps up' the amount of assist more slowly than it did before when starting out/pedal pressure is low to get a more natural "bike that helps you" and less "pushy" feel.