ᐅ Any experiences with purchasing batteries with more than 1 kWh capacity?

This is not about making a prediction. It's about whether the sizing matches the scenario. A 3-day power outage and a 5 kWh battery do not fit together; you need to go much bigger.

Exactly that.
Either do it properly so that you can cover several days, or not at all.
Keeping power for 2 or 3 hours is nice, but nothing more.

I would rather use camping equipment (stove, lamps, propane infrared heaters) than spend so much money on batteries that I hardly ever need. It’s much cheaper per €/kWh. Plus, boiling water is easier and more practical with gas than with electricity. Ideally, you have a caravan – they also have gas-powered refrigerators, but that will be a minor issue in winter if there’s no power supply.

Otherwise, a portable photovoltaic system, a suitable charger, and an e-bike battery that isn’t locked to a specific brand or device. You can connect anything up to 36V, or use an inverter for 220V appliances if needed.