Play music from laptop over WiFi to existing audio system: how?

But I would imagine the audio quality of wifi connection would be inferior to that of USB simply because of the unstable nature of wireless connection. 

I cannot hear any difference. My WiFi handles up to about 1 Gbps. CD quality PCM audio over TCP/IP requires only 1.4 Mbps I think. I know it's not just bandwidth, but jitter that matters too.

I am using my PulseAudio "free" solution right now and it streams PCM audio over the network. It sounds the same as the USB cable to me. My speakers are Magneplanar 1.7i. My DAC is Onkyo P-3000R. WiFi playback has been flawless all day since I got this working.

It is wild that one can do this correctly and cost effectively so many ways using the right software on the right general purpose computing devices or buy expensive dedicated devices designed just for streaming that can cost so much more. I’ve found just use the right DAC that sounds good to you and good quality streaming software and you are in business with very high sound quality these days. Son much easier and cheaper than getting a good quality phono setup and keeping it that way. All my records and tape go straight to my music server when played these days and then they then get the nice retirement that they well deserve.

Here is yet another solution:
W3 Wireless Audio Adapter — Audioengine https://audioengineusa.com/shop/adapters/w3-wireless-audio-adapter/

From my experience you have two routes depending of what it is you want to achieve. If you really mean that you want to play from your laptop to your hifi using wifi then products like Apple Airport can do the job. That is where I started. However, that means that your laptop or phone actually is playing the music, which is transferred to your HiFi. It eats battery and eventually your music stops if you for example see a video on Facebook.

A much better solution is using a streamer, which is connected to your router and your HiFi. In that case your laptop or phone is your remote control. You will need a streamer (transporter so to say) and a DAC that converts the digital signal to the analog amplifier. You will find solutions for this, which ranges from 100 to 10.000 $. 

A requirement for me was that the streamer could do Tidal - you need to consider if such is a requirement. 

I started off with a simple solution based on a Teufel streamer and a Musical Fidelity DAC. Total cost of 500 $. Recently I upgraded to Innous streamer and RME ADI-2 DAC. The intent still to stream Tidal, but use Roon as well. Total cost around 2.000 $. 

@mtraesbo I do like the suggestion of using my laptop (or phone) as the remote control. I already have all the hardware required in that case. I do not even need a wireless streamer. All I need is the right software to make the phone or laptop act as a wireless remote control. Unfortunately, that is where I keep running into a roadblock because I don't want to get involved with any of the commercial solutions I have seen such as Roon.
I want a solution that is totally local with no meta data or any other private information going to some third party. I'm checking to see if any of these options meet my requirements:
10 Best Media Server Software for Linux in 2018 https://www.tecmint.com/best-media-server-software-for-linux/
In regard to Tidal, some of the media servers listed at the above link offer it, but I don't need any streaming services. I will only be playing my own music which is stored locally.
My "temporary" and free solution has been working well. It's the solution based on PulseAudio. It does stream wirelessly from my laptop to my DAC / preamp (Onkyo P-3000R). In that regard, it is not as good as your suggestion.  If I can shift to using my laptop only as a remote control, then the next step I would like to implement is multi-room playback.

I can currently do multi-room playback with PulseAudio, but because it is streaming uncompressed PCM data to multiple rooms, I am having a few minor quality issues. I may be able to solve those, but I will still need a wireless remote control, as per your suggestion.

Alternatively, I might have to revisit my original idea, the Yamaha WXC-50 and their MusicCast system.