It seems like you covered the most important part in your answer. One other idea could be to place the router as high as possible but also to use some kind of app to check the signal strength to find the best spot for your router. And, don't place it too close to your microwave if you use it a lot since they both operate on the same frequency.
As was already stated in the problem description, I would again check the positioning of the router. Are there any objects, big or small, in the way of the signal going to the second upper floor? Such objects could interfere with the signal strength. Think of the Wi-Fi signal as beams of light originating from your router that get reflected on each surface until they finally reach your PC or laptop and try to optimize it that way.
Furthermore, you can check your router’s settings for it’s channel settings. To prevent interference from your neighbours Wi-Fi sources the channel settings should be set to “Auto”. You can also try to set it manually, but I would recommend scanning all for Wi-Fis beforehand, with an app like Wifi-Analyzer.
There are also hardware options if you are willing to further invest into better Wi-Fi coverage. Simple Wi-Fi extenders like this one can be placed around your flat to amplify your signal by placing them at key points, e.g. near the stairs where signal might still be acceptable. Also, there are Power-line adapters that modulate your internet communication onto your power lines within your home. These can be hit and miss and depend on your home’s power lines.
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In a two-story home, the router should be located at the lower floors ceiling or the upper floors floor, as the signal radiates from the center of the router [1]. Very important is that the router is not hidden behind any obstacles (e.g. positioned inside a drawer because you don't like the looks of the router). Another important thing is, that it is not hidden hehind books, as books are very strong isolators for wi-fi signals.
I personally have used wi-fi repeaters (like [2]) to strengthen the signal. These should be placed in the middle between the router and the place where you want to access the internet.
[1] https://www.howtogeek.com/428216/where-to-place-your-router-for-the-best...
[2] https://at.avm.de/produkte/fritzwlan/fritzrepeater-2400/
it could be also possible to aim some of the antennas of the slightly towards the ceiling. But you still won't have a good coverage directly above the router