Hi duvan,
Lots to unpack there. Sorry for being long winded.
I'll focus on my expertest as someone with 3+ decades of network / compute experience. Wifi and audio are not great. Be it Bluetooth or any wifi protocol. It's getting better, but it has inherent problems. I speak in general terms.
Networking introduces jitter and latency in the time domain. Remember the old days of VoIP. It sounded like crap compared to a landline, but it improved. Human hearing is very sensitive to time domain delay. So any deviations in this domain, effects what we perceive as quality sound. Room acoustics included.
Generally if you direct connect via RCA, Toslink, CAT 6 or other physical media you will get wirespeed (just under light speed) there are lots of factors here. However, the latency you have on these medias (physical) is vastly less than wireless. As a result you will have far less "sync" problems.
There are many protocols (software) that attempt to adjust for this. Some more successful than others. Most consumer (home) products may not even try but more influence on the codec. This is why say the latest Cisco 9K switch costing a few thousand dollars vs a consumer switch which cost a few hundred... among other reasons.
Wifi and bluetooth make it even worse, you're not traveling on a physical media, so you are competing with other devices and thus latency, ie: phones, IoT, laptops, etc. which impacts latency and jitter, regardless what the marketing / sales people say. Bluetooth is what we call in the industry as very noisy. Introducing noise, drops, collisions, etc. all bad for audio. Have your earbuds ever dropped out from time to time on your phone call?
Add all that, to a clock signal. Most computers or DACs, don't have good ones unless you buy them. Add to that, RF (Radio Frequency) noise, effectively anything electric and you are faced with many more issues. Really and argument for quality cable shielding.
Basically, a physical media will always perform better than wifi or bluetooth unless there are leaps in consumer networking.
Your bass issue is a bit strange. It could be that the "compensation" algorithm is reconstituting the bit stream to what it thinks it's right based on a CRC or other criteria. This has little to do with bit rates, or sample rate, or codec, other than more, means you need a faster media.
My advice is to avoid wifi unless you just want to use headphones perhaps, you will never hear it given the range from connection points, unless everything is on the same network (a single vlan has it's own problems) and you are dealing with video and audio at the same "sync" time it can get "noisy". Remember Access points (where your wifi base lives) effects things too. Long ranges affect the bit stream as well. I hate to say, bit's are bits, but the medium is your weak link. WiFi is worse, so avoid it if you can. I'm sure people will argue otherwise, but it's your propagation media matters.
Remember, if you live in a congested area, your neighbor's wifi is also be affecting things. A simple phone app will show you how many items are competing for the same frequency range and channels as your devices. All will add artifacting.
Long story short. If you can run the cable do it. Most of your problems will go away.