Why is that required? Switch to three phase? Wasn't required for me in the UK.

No. Everything in Germany has been three-phase since forever.

But especially with old houses, with any "not insignificant change" to your electrical setup, you have to bring everything up to modern standards.

Also, and connected with that, metering is weird in Germany. If your consumption rises above a certain amount (I think 10MWh for a single-family home) you are required to get a "smart meter", meaning a digital meter which includes the possibility (just the possibility, not actually the real thing) of online reporting and minute-by-minute pricing. In the rest of the world, that would just be swapping the meter or slapping some Wifi-to-IR-interface on it, but not so in Germany. You need to install a new metering cabinet that provides space for at least one digital meter (but better provide more than one...), one remote control receiver (for old-style night/day tariff switches, obsoleted by smart meters but still required nonetheless) and a smart meter gateway. That new metering cabinet needs to conform to standards set by your local electricity supplier (which can be as small as a city), so there is no nation-wide standards, more like 50 of them. And the metering cabinet is huge, not someting like the 30x40cm thing you see on sidewalks in spain or something, no. More like 200x140cm in the smallest(!) version. So those are really expensive just because the market is tiny and the requirements are completely crazy: Even though most smart meter gateways are wireless nowadays (UMTS or GSM) and usually such a gateway won't be installed anyways (because just the possibility of installing one is required), you also need to provide for cabled internet uplink to the metering cabinet. That uplink is a Cat6 cable to the gateway, but it crosses through the electrical uplink part of the cabinet. So the insulation of that cable has to be certified for at least 10kV insulation voltage, at least 80A current on the shielding and more stuff like that. So e.g. just that one stupid half-meter Cat6 cable will set you back 50Eur. Installation isn't any less crazy. You definitely cannot do anything yourself. Even your licensed electrician can only do the menial preparations. When your licensed electrician is done with the prep, you request an appointment with the local supplier's meter installer, who, after a typical wait time of 2 months, will install and seal the meter in the presence of your licensed electrician (who is there to receive complaints about incorrect prep, followed by another 2 months wait time for another appointment...).

That's why it's 4kEur...

And if you want your power to be a few cents cheaper (28ct/kWh instead of the usual 35ct/kWh), you need an extra meter for your heat pump. Have solar? Another extra meter. Want to charge your electrical car? You guessed right. And you cannot bring your own. Each of those "smart" meters has to be rented from your local supplier at around 20 to 120Eur/year.