Maybe try wiring either the Playbar, or the Office Play:5 to the ‘primary’ Nest Hub/Router to switch all to a SonosNet connection to run alongside the mesh WiFi and see if that resolves your issue. 

Ken is right.  You must first stop factory resetting unless someone who knows what they are doing asks you to.  This usually is at best a waste of time.

It sounds like your network is badly configured and you have (accidentally or deliberately) split your system into two.

I assume the primary Google device is wired by its WAN port to your router?  Is anything else wired to the router?

As a temporary measure, move the P:5 (if necessary) to a few feet from the primary Google device and connect the two by Ethernet.

Your router needs to be in modem only mode.  Is it?  If it does not have such a mode, please disable DHCP in the router settings, and also disable WiFi on the router.

If you can get that far and answer my questions we can carry on and get this sorted.

The router is in modem only mode, with no wireless at the moment, nothing is connected to it aside from the google wifi.

I have attached the ethernet to the play 5 as suggested, and has updated from WM1 to WM0 as expected.

That’s great.  Now I am going to ask you to power off your Arc and surrounds.  Then power up the Arc, and factory reset it in the process (trust me).  Leave the surrounds powered off for the moment.

Then go into the Settings in the Sonos mobile app and choose ‘Add Product’.  If at any point you are asked to choose between  “add to existing system’ and “set up new system”, choose existing system. Do NOT set up new system.

Follow the prompts and see if you have a unified system.  Your system should contain two “rooms” representing the Arc and the P:5.  Both should show WM;0 in About my System

The Arc has been reset and during installation received the message ‘ Your Sonos Arc has been added, but may not appear in the System tab.  If so, Unplug the power cord and plug it back in to finish setup from the System tab.’  After doing so it appeared as ‘not registered’ and then added to the Living room.

Then got an error saying it could not find the Arc and that it would need updating.  Quitting the app and opening again and the Arc appears.

Both the Arc and Play 5 are on WM:0

Can you play music through them both (individually and grouped)?

only the play5 - for the arc ‘Unable to connect to Sonos product’

the arc/living room has now disappeared

The arc returned by itself an started playing a random song from Amazon music.  I was able to control it and also group with the play 5 and have the same song play over both locations. though how long it would stay connected/visible is a concern.

Is it still on the network and just missing in the Sonos App - can you ping its IP address? If so, try this:

1. Remove the WiFi credentials from the Sonos App. See this link: https://support.sonos.com/en-us/article/remove-a-wifi-network-from-your-sonos-system
2. Try a different SonosNet channel in ‘Settings/System/Network’

It last about ¾ a song before the arc disconnected.

There are no networks currently setup, it is on the SonosNet channel 6, which i have just changed to 11.

I can move the play temporarily closer to the arc if required, but again only temporarily while i get it back on wifi.

Please leave the Play:5 wired for now. Please would you run another network matrix and post it?

Sorry I meant i can leave the play 5 wired but bring it physically closer to the arc if necessary for a short time.

Network matrix option is unavailable - the only options are:

Office (RINCON_347E5CD453CC01400)

Zone Player Info
Ethernet Ports
/VERSION
/proc/ath_rincon/status
/sbin/ifconfig
/usr/sbin/brctl showstp br0

finally both appeared at the same time:

Thanks.  Is that the colours it actually appears in?

The signal strengths look quite good, but it would be worth moving the P:5 to see if it being affected by local interference.  Keep it at least 3 feet from any Google puck.

Also worth experimenting with changing the wireless channel used by Sonos.

yes they are both in yellow on the matrix. the arc keeps disappearing, but seems better on the selected channel.  yet to add the surround or attempt to migrate to wifi network.

Long experience of cases on here suggests that Google mesh WiFi and Sonos on Wifi are not happy bedfellows.  You have a much better chance od a stable setup if you continue to use SonosNet.  As neither of your speakers can be conveniently wired, this would mean buying a Boost, but I’m reluctant to suggest that until the current temporary arrangement works better.

I am puzzled by the Arc dropping out still.  Possible causes are:

1 Wireless interference

2  IP address issues ​​​​​​​

3 Hardware fault

We could spend ages getting nowhere trying to disentangle that.  I suggest you now submit a system diagnostic immediately after a drop and call Sonos Support with the confirmation number.

You could factory reset the Ones and then add them as surrounds in the Arc’s settings.

I think we have made worthwhile progress and got things to a position where a diagnostic is worthwhile.                                                                                                                                                                                                                                                                                                                                                                                                                                                                  

Further thought: Before you do anything else, it might be worth a final reboot of the whole system.  There has been a lot of chopping and changing, so I would power everything off, and then in this order reboot everything: router, primary Google puck, Play:5, Arc.  It may not male a difference but you never know.