What exactly is a smart home and can it be retrofitted?

Most consumer-grade systems fail even in the reliable detection of presence/absence. Not to mention the detection of whether the present person is authorized and I’m not even talking about the recognition of activities and states — these systems are far behind, or haven’t even come up with the idea that this functionality is needed.

These requirements are not even being demanded!!! So why use a sledgehammer to crack a nut when the OP just wants a bit of "play" and experimentation.

... or voice control. ;)

That’s again putting the cart before the horse. I explicitly refrained from including that in the list because it was meant figuratively. Because you can also tinker voice control onto a rotary dial. It’s an add-on. 95% of rotary dial users are convinced of that.

I don’t think I need a "real" smart home.

Since everyone understands something different by that and apparently you have no idea at all what lies behind the term....

I wanted to forego things like motion sensors because I have a big dog who would probably trigger them constantly.

Possibly, especially if the dog is 2m tall. And is the dog constantly on the move? No minute of peace? And does it run through the whole house all the time and would keep going into adjacent rooms to deliberately trigger the sensors again and again?

I find the enocean technology interesting if there is no power supply at that location.

It’s usually only interesting until you’ve seen the switches etc. in action and then realize they are far removed from the usual and familiar way of operation in terms of haptics, optics, and acoustics. But yes, for the garage or attic it’s great.

What’s important to me is that everything still works old school via button press.

That’s completely overrated and that’s where the root of the problem lies. But yes, everything is possible. If the customer wishes and brings the money, then he gets many superfluous buttons exactly where he wants them.

but also works with rules and small automations

That’s where it starts to get interesting.

my demands apparently aren’t that high

You simply have no overview yet of what is possible/would be possible and you’d need thorough advice. Your wishes/requirements are more or less raw.

As for example:

Roller shutter control with rule creation, e.g., always go down 30 minutes after sunrise but not before 7 a.m.

And when should they go down? And if you want to go through the door before/after sunset? Operate everything by hand again or wait until the time has come? Then why bother at all?

Light control via phone or voice (Philips Hue lamps for Ambilight will be installed in the living room)

Usually causes more hassle than it appears and then nobody really uses it anymore, only very rarely after the initial hype is over. Operating anything in the house via phone is seldom comfortable. Because first you have to take out the phone, unlock it, open the app, etc. Voice controls work similarly.

Window sensor for the sliding door so my roller shutter can’t just lock me out

One is not sufficient. Or only conditionally. And only for the roller shutters to be controlled by it is casting pearls before swine.

Video doorbell that notifies me on my phone when I’m home

Looks nice in advertising. In reality often the complete opposite, but yes doable, although a lot of money can be sunk just to have this one possibility which I always find incomprehensible.

Smart music system in the living and dining area for, e.g., internet radio

Also here a lot of money needs to be sunk and also here smart is not just smart. What else should it be able to do? Because internet radios are nowadays available off the clearance table.

maybe later also control of underfloor heating

What should be controlled exactly or what should be regulated at all? (Those are two different areas of responsibility).

I thought if I could control the blinds like that, it would already be smart :)

We are currently building a house from a developer; he told me that smart home can be planned with the electrician, but the problem is we get contact with the electrician very late, then you have to decide quite quickly

All the standard light switches are already included in the price

What kind of smart home would you recommend to me? The surcharge should not be too high or as low as possible because many other things are still pending and eventually the money runs out :)

If you want to do things directly during construction, you would probably have to postpone other things again

What is also very important to me is that I can create new settings or rules automations in the "Smart Home" myself or change and configure existing ones myself.

I do not want to have to call an electrician or similar for changes.

I thought if I could control the blinds like that, it would already be smart :)

You’re not alone. The overwhelming majority of all "Smart Home" fans already consider the app for their Hue bulb to be smart. It’s nothing more than a dumb remote control. In the past, there used to be something like this as a remote socket at the hardware store; today it’s called Smart Home...

What kind of Smart Home would you recommend to me?

There is no "the" Smart Home. It depends 100% on your budget and the effort you or your electrician want to put in. And effort is pretty much synonymous with money when it comes to electricians.

The extra cost shouldn’t be too high or should be as low as possible because many other things are pending and eventually the money will run out :)

Are you an Apple user? Then you could take a look at Opus GreenNet. At first, it can simply replace all your switches and later can be expanded with a gateway, e.g., to HomeKit or other apps (yes, also Alexa). The switches are initially a bit more expensive, but then they are already there, and you can also form groups of blinds or similar without a gateway or other intelligence. Otherwise, there is nothing remotely price-neutral. Fun costs money. Alternatively, you could work with Shellys; I can’t think of anything cheaper. Homematic could also be an alternative... a bus-based system would absolutely not fit into your budget, so you should probably look directly at wireless and choose a standard that is as open as possible. And most importantly: Your electrician has to want it. Many general contractor electricians simply have no interest in deviations from the standard. Unfortunate for the customer, but that’s often how general contracting works. So I would clarify that beforehand.

Is that a developer?
Then you don't have much to say anyway, and if construction has already started, it's actually too late.