I strongly recommend a proper wifi solution. You are asking for trouble with repeaters and even more so with using a microcontroller as your repeater. ESP’s aren’t known for throughput so they would be a HUGE bottleneck. They have been tested to a max of 303 Kbps. Not the speed you are likely looking for especially since it would be cut in half to repeat.
Wireless systems are far more complicated than people realize. The common solution to poor coverage is to use extenders or additional AP’s.
Extenders are the worst. They suck off of the existing AP making it slower instead of introducing more capacity to your network. Often they have a new SSID_2 network or something. This confuses people and devices. They won’t naturally transition from one ssid to the next. I would avoid extenders until they are your absolute last resort. Since you have a robust wire network, definitely not a good choice for you. ESP as extenders is the ultimate in worst IMO. They are cheap chips built for simple wifi connectivity.
Additional AP’s are the way to go BUT it must be done correctly. The common path people take is to go out and buy an additional (or more) residential grade ap’s and pepper them around their house either with the same ssid or SSID_2 (same applies to repeater here about device/human confusion). There are two major issues with this:
1, residential grade devices aren’t very good. They are built cheaply because consumers don’t want to pay what a quality AP costs (another reason why a cheap esp is a BAD idea) as well as they are usually a router, switch, ap and gateway in one even though you only need the ap and switch portion.
2, they don’t talk to each other.
Without getting into nitty gritty, each AP needs its own channel to broadcast on. I’ll stick to 2.4ghz (US, I don’t know German channels) for now. There are only 3 channels for 2.4ghz that don’t interfere with each other (1,6,11). That means you can have a maximum of 3 AP’s in range of each other and set on 1, 6 and 11 without them causing each other to slow down from interference. If you have a super large area, you can have many more AP’s than 3 so long as an ap set on channel 1 isn’t within range of another ap set to channel 1. Many people think setting your multiple ap’s to all use the same SSID and Channel is the proper answer. It is not. Trust me Oh, and don’t forget your neighbors. If you live in a rural residential setting, you probably will see one or two of the channels used. In an apartment… good luck, they are all used, definitely use 5ghz.
Back to the not talking to each other part. Say you setup 2 ap’s on non-interfering channels both on SSID1. You connect your laptop to SSID1 upstairs and it gets the upstairs ap. You then move downstairs. Your laptop is now sitting inches from your downstairs AP but since it can still see the broadcasting upstairs ap it already negotiated with, it stays connected. You could theoretically walk to the curb and still see the upstairs ap so it is going to fight tooth-and-nail to stay connected to that upstairs AP. With a proper mesh network, the two ap’s would talk and a hand off from the upstairs ap to the downstairs ap would be seamlessly carried out.
OK, enough boring stuff. My recommendation… entry grade pro IT wireless. I personally like Ubiquiti. It looks as if they are available in Germany. There is a community post on the forum about a guy’s setup in Germany…
You can grab a Unifi UAP-AC-Lite for 80-90 USD. So for about $160 you could have 2 ap’s that will cover 3000 sq ft very well. The controller software is free and can be installed on anything you like as it only needs to be on when you make changes. I see you run esxi so slap it in a debian vm… The ap’s come with poe injectors so you can power them from your DMARK. I have a large UPS that holds my AP’s when the power blips.
Hope this helps.