Help me upgrade my beginner system!

I would put it all in new speakers.

Go for high sensitivity (less power needed) so you can more easily try tubes someday.

My preference: no passive radiators, no ports, IF port front facing.

I would try to not need a subwoofer, if sub make it a stereo pair of self-powered subs, located adjacent to the FL and FR.

Some low bass starts mono, however the overtones progressively/quickly become directional

Used speakers can get you more: IF you are careful, and if close to you to listen, avoid shipping.

I would sell everything first (while saving other money). Then, when you know how much you have, see what available speakers appeal to you, ask here about them.

Your TT and Cartridge are darn good. Replacement stereohedron stylus/mono stylus/78 stylus all fit that cartridge body, nice optional duster ...

https://forum.audiogon.com/discussions/is-a-ortofon-black-a-step-down-from-a-pickering-xsv-3000

amp powerful, MM phono built in,

Yes, loudspeakers first.

You never listed the gear from your brother that you are looking to trade in/sell?  I’d ditch the power conditioner as well, I feel that they rob the music of its emotional content.  I’m also a big fan of tubes, so a nice tube integrated amp would be on my list if it were me.

Speakers if your room is buttoned down

Looking over your system, looks like you did a good job of choosing… looks well thought out. I also think you are correct the DAC probably has the biggest opportunity for improvement.  I recommend looking at a Schiit Yggdrasil. This is in your price range and is comparable to DACs at higher prices.

Spend time working with speaker placement and room treatments. They can be less expensive by using carpets or real purpose built acoustic treatments.

If you added a Yggdrasil, then all your components would be performing at roughly the same level and the next move, should you want to would be raising the whole system to the next level which would be 1. Speakers, 2. Integrated amp, 3. Streamer, 4. Power conditioner. My rule of thumb for this “level uping” is each new component should be no less that 2x an investment 3x is better. While this would could be one component at a time. The resultant system would be very substantially better.