Without eARC, lossless multichannel signals will exceed the bandwidth limitations of ARC. This is not an issue concerning lossy signals like Dolby Digital, Dolby Digital Plus and DTS. Smart TV service apps will stream lossy DD and DD+ signals so no issue there.
Is there a 4K blu-ray player, PS5 or XBOX Series X/S connected to the TV here? They will require eARC support in both the TV and receiver to pass lossless multichannel PCM, Dolby TrueHD and DTS HD MA as you already know and a device such as the one
@TLS Guy linked will be required to get lossless multichannel audio from the TV to the receiver.