Sonos (Turntable / Yamaha Integrated Amp) Advice

That's a different delay, caused by receiver DSP; it would be caused by the speakers wired to the receiver getting their signal later than Sonos speakers, both being supplied by a Connect. I do not think that applies here because the amp in question is a stereo amp.

The sync issue that the OP should be seeing will be due to the receiver speakers playing before the Sonos speakers. That cannot be corrected by any adjustment in the receiver and will get worse if Connect Line in is set to compressed mode.

Digressing from the topic, I wonder if this can be a solution, perhaps partial, to the issue of delays from using a Connect into an AVR using its processing modes. Have the two delays cancel each other, although I suspect that getting echoes to vanish will take more than partial cancellation.

On my Yamaha, an older RX-V661 there is a slight delay in some of the processed audio modes where the receiver is altering the audio. In Pure-Direct there is none, the others vary from unnoticeable to barely noticeable.
Same for me. Ten year old Yamaha AX-757SE: no percpeptible delay when using its (processed) 2-CH and 7-CH stereo modes. The message is not to assume there will be processing delay problems without first verifying it to be the case.

From a previous question. When I'm plugging the Connect. If i'm doing the second option. Can I just plug a Coax into the Coax of the receiver?

Say my Phono is going into Line 1 Input. Should I run RCAs from Line 1 Output to the Connect and plug the Coax to the Coax of the receiver? Or should I run RCAs from Line 2 Output from the receiver into the Connect Input?

Sorry confused if I am supposed to share the same Line.

Coax and optical are both digital outs. When you use a digital out on a device, you are simply using the device as a router to deliver the original digital signal/file to the receiver. The direct signal/file is then decided to music using the receivers digital to anologue converter. If your receiver has a better DAC than the Connect or it has DSP then you will get better sound using the digital out on your Connect.

The answer to your question Is, if you use the digital input, it isn’t going to matter. Likely the digital input is the AUX setting. Your receiver should output that signal on all outs. On your receiver, the out channels were designed mostly for the cassette tape and VCR recording days. Today’s equipment usually have analogue signal outs and channel preouts.

On my Yamaha, an older RX-V661 there is a slight delay in some of the processed audio modes where the receiver is altering the audio. In Pure-Direct there is none, the others vary from unnoticeable to barely noticeable.
Same for me. Ten year old Yamaha AX-757SE: no percpeptible delay when using its (processed) 2-CH and 7-CH stereo modes. The message is not to assume there will be processing delay problems without first verifying it to be the case.

This is my experience also. I run my receiver in 7ch stereo with the digital enhancer on using optical input. I have no perceptible delay in the playback between either of my connects and receivers and the other Sonos speakers in the house.