Confused if I can get 5.1 audio from the components I am buying.

[AffectedRyan]

So I am finally making the jump to 4K HDR movies for the family in the living room. We don't have much to spend so that is reflected in the components below.
For some reason, I am having a hard time figuring out if I should go with a cheap soundbar or the 5.1 system I have linked down below.

I hear TV's don't output 5.1 via the optical in some cases and in other cases I hear I need ARC in the TV for it to work over HDMI.

What I would like to do. We consume mostly all of the HD content over Netflix but also stream video from my PC to this new set up as well as the other two Chromecasts in the house that are connected to only 1080p Tvs and Regular Chromecasts.

Audio http/

TV http/

Casting http/

For this setup, I would like to plug the Chromecast Ultra into the receiver and have it go to the TV all while getting surround sound from the receiver. Will this just work?
Do I need to run an audio cable as well from the TV back to the receiver?
I don't really need help finding different components so thank you to everyone who would normally say "Why those, get this".

Alternatively, I am aware it is a smart TV and I assume the Netflix app would have 5.1 from the TV to the receiver via optical but I would like to keep the TV to the Chromecast HDMI full time. We have two small kids and the whole house Is set up with Google homes. I love how they can play what they like, pause etc, as well as one, is learning about the weather and it's nice having those things display on the screen while he learns.

Thanks in advance and sorry for my ignorance...

 

[americanaudiophile]

You don't sound ignorant just a bit unsure.
You won't need to run an additional cable from the TV to the receiver. You could use HDMI-ARC if you wanted audio from the TV tuner or apps to play through the receiver. ARC and the optical output won't handle lossless audio codecs such as Dolby TrueHD or Atmos but are fine with regular Dolby Digital. I doubt you will find a TV that doesn't output in bitsteam but you can check for that in the Sharp owners manual.
If the Chomecast Ultra (and any other source) is connected directly to the receiver than than you will get whatever audio the content and provider offer without the TV being involved at all.
I would go with the Pioneer set up rather than a soundbar. It will give you much better surround sound. It can also be upgraded piecemeal if you want to. Better front speakers would improve the sound greatly.