Recommend speakers for a large living room

dpal, your 'living space' is as large as one of my shop buildings sans restroom. *L*  A lot of air in there.... ;)
You haven't mentioned ceiling height(s), which in that large an area will effect what anything will sound like.  Just be aware...

Since all your windows are on the west wall, I'd like to suggest a different approach based on the noted 'use areas' in the floor plan.

Have a 'Nice' pair of speakers flanking the windows; it suggests having a drink, preferably with the significant other, watching the sunset or the view you're paying for. ;)  Subwoofer optional...*S*

The wall with the 2 circles could have a flat screen of your choice flanked by a front pair with a back pair by the same manufacturer.  An obvious location for the 5.1 system.  If you opt for Ohms, you shouldn't need a center infill, but a small sub would be terrific.  The back pair, also Ohms, could be smaller to be less intrusive, flanking the sofa.

You could drive both arrangements with a single 'well bred' receiver with a decent speaker selector.

As for the rest of the rooms, Bluetooth as desired, unobtrusive as possible.

Careful shopping ought to keep within the budget. *G*

All I'd ask is let me come listen someday...;)  I'll BYOB to share...

Oh, the Ohm/Walsh 5.1 ought to fill the main space nicely.
Mine does. *VBS*

I would also echo the recommendation for Meridian digital active speakers as suggested above.  In addition to the DSP8000s, you can also consider DSP7200s and their Special Edition variant which will fall within your price range.  Worth a listen and consideration.

A little "out of the box" thinking here. :)

Given the size of the room and the hardness of the surfaces... why not use a myriad of well placed ceiling speakers,. with the requisite number of subs at floor level?

https://www.youtube.com/watch?v=x2ch8aQLwUY&app=desktop

Found this link that describes spatial qualities... see end of video for Laufer’s explanation.