Your Onkyo doesn’t seem to support LDAC Bluetooth codec, which means the Hidizs would need to use a lossy compression algorithm to send the audio to your receiver. Not exactly ideal.
There are two ways to cut down on the cord length. You can connect a streamer to the Modi 3 or you can connect your receiver to your network and stream directly from the PC to the Onkyo. Either method would utilize a protocol called DLNA / UPnP which is lossless and bit perfect.
The streamer can be a PC that you don’t use a lot anymore or something like a WiiM Pro or a Raspberry Pi. The WiiM Pro would be the easiest to set up. Just connect it to your network and link it to the Modi with a digital coax cable.
Alternatively, you can connect your Onkyo to your network and send the audio directly to your receiver. Unfortunately, this also means you’re completely bypassing the Modi 3.
If you want to stream from your PC, I suggest a Windows app called Stream What You Hear (link). This sends all your computer audio to a DLNA / UPnP device.