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

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.

@lowoverdrive: for < $130 you can build your own with a RaspberryPi 3B+ ($40), HiFiberry Dac+ Pro ($45) as HAT, and all that in a HiFiberry steel case ($30). Throw in a few copper heatsinks for the RPi 3B+ board. ($5).

Then (all free): Volumio as your primary OS _and_ streamer/player, and BubbleUPnP for Android as your control point (or some other control point app - will talk to Volumio via UPnP/DLNA), and your existing laptop basically as NAS (or control point + NAS).

Fun lil'project, great network HW on the RPi 3B+ (Gigabit ethernet and 802.11ac wifi), Hifiberry DAC+ Pro hard to beat for ~$45, Volumio dead-simple ... and all kinds of entertaining and useful extension later (like: set up for multi-boot using Berryboot, then switch bet. Volumio, OSMC/Kodi as media center, and Raspian for all your Linux stuff).

@usery I know about the RaspberryPi and HiFiberry Dac. I’m concerned that won’t give me the sound quality I’m seeking.

However, the approach of using a general purpose computer running some Linux flavor has become my preferred option. I just decided to go with more powerful CPU’s and better DAC’s.

In the last few days I extended my system to whole-house music playback. My favored music player is cmus, something I just discovered while working on this project:

CMUS (C* Music Player) - A Console Based Audio Player for Linux https://www.tecmint.com/install-cmus-music-player-in-linux/

Each room now has a laptop (connected via wired Ethernet), a USB DAC, a power amp and speakers. Here’s how it is organized.

- home network extending to each room, where I have:

• laptop
  
• USB DAC
• power amp
• speakers

each laptop which is connected to speakers runs:

• Linux
• PulseAudio
• ssh

one computer on my network also runs:

• tmux
• cmus

The above computer has all my digital music files too.
I can control playback from any computer on my network, including a laptop over WiFi. I could also use my phone as a remote if I wished, but so far I haven’t felt the need.

The beauty of this approach is that it is very simple and very flexible. The simplicity surprised me.
.

lowoverdrive 

... I know about the RaspberryPi and HiFiberry Dac. I’m concerned that won’t give me the sound quality I’m seeking.

You may be right. But don't underestimate the Raspberry Pi. When configured with the Digi+ S-PDIF HAT and run into a high-quality outboard DAC, it can produce astounding results - especially for the money.