There's a lot to respond to in that post. I won't try to answer every question individually, but I'll try to provide an explanation that might help you understand streaming systems.
Firstly, let's start with the music library. There are two aspects to this; 1. the physical library, consisting of a set of media files on a storage device, and 2. the logical library; essentially, a database of information about the physical library, maintained by a media management tool, such as Plex or MusicBee.
You can modify the physical files using one of a number of media manager tools, e.g. to change metadata, add artwork, change file location, add volume levelling tags, etc. If you use multiple media management tools on the same physical library, the others will usually automatically pick up any changes made by other tools. I use MediaMonkey and MusicBee to manage my physical library.
Now, it is possible to get multiple instances of a media manager (e.g. on laptop and PC) to access the same library database; I believe this is true with MusicBee, but I don't do that; I create a logical library on each on my machines. You would need to store the database file on your NAS, and point the multiple MB instances at that file. I'm not sure that it could cope with concurrent use of multiple MB instances (they'd fight over the file). Search the forums for threads on such shared logical library database. But you can have Plex and MusicBee accessing your physical library at the same time, without any problems.
Now for the streaming protocols... Let's start with some basics:
A Digital Media Server (DMS) stores your media, catalogues it (using metadata) into a database, and streams it to devices when instructed to do so.
A Digital Media Renderer (DMR) takes a digital stream sent to it, and converts that stream into audio, or still or moving images.
A Digital Media Controller (DMC) interrogates the database held by the DMS, and allows the user to instruct the DMS to stream selected media to one or more DMRs.
Things get complicated by Digital Media Players (DMP), which can combine DMC & DMR, or sometimes all three DMS/DMC/DMR. One can think of an MP3 player as a DMP of all three parts, but very closely integrated.
All this relies on the availability of a data network, but, since you already have the Chromecast Audio DMR, and you're posting on the internet, I'm going to assume you have that...
DLNA is a widely-adopted, open digital media networking protocol (initially developed by Sony, but made open), providing the three functions of DMS, DMR and DMC, and is supported by a huge number of media devices and servers. Airplay is Apple's, proprietary digital media networking protocol.https://en.wikipedia.org/wiki/Digital_Living_Network_Alliance
BubbleUPnP is an Android app that can provide all three parts of a DLNA system, or any subset. I use it as a DMC on my phone, accessing the Twonky DLNA DMS on my NAS (a bit like Plex on your Synology). The phone controls the Twonky DLNA DMS to stream media to any of the DLNA renderers around the house, some of which are BubbleUPnP apps running on Android media boxes. BubbleUPnP, running on an Android media box, can also act as a DMS, indexing a physical media library on an HDD attached to the media box.
BubbleUPnP Server is a program that runs on PCs, NAS devices, etc. It is intended to provide support facilities for the BubbleUPnP app (or other DLNA services). One of these services is to provide a virtual DLNA DMR that casts to a Chromecast audio device. Bubble Server also provides transcoding and remote access to a DLNA DMS (from outside the local network).https://bubblesoftapps.com/bubbleupnpserver/
Don't worry about the route data takes; it remains in the digital domain until it reaches the DAC, so is not degraded like analogue signals might be; that's the major benefit of digital transmission systems.
I prefer MB portable install, because it keeps all the files in one place; on a conventional install, they are spread over multiple, obscure locations within Windows application directories. I like to be in control, or at least know where to find things...
I can't help with the subsonic plugin; I've not used or looked at it.
Hope this helps.