A streaming setup that competes with my CD and turntable set up?

I have just started to listen to music again. I am very happy with my current set up. I have a Cary Audio 303 cd player and a Well Tempered Classic turntable with a Bottlehead Eros for a phono preamp. I want to mainly stream with tidal and listen to music that is not in my current collection. My question is ... would a simple set up like an ipad or mac mini into a couple of hundred dollar dac get me close to the sound quality of my current sources? If not, what would it take on a budget to get close to the sound quality that I'm getting currently? Thanks in advance.

what would it take on a budget to get close to the sound quality that I'm getting currently?

Define "close". Because it seems to me no amount of money is enough to get digital close to vinyl. But digital includes CD players, which you threw in there as if you consider your CD not only "close" but the same as your Well Tempered rig. Which I find highly unlikely. I mean, that its close. But that's me. Not you. So the question is, what exactly do you mean by "close"?

Alternatively, yeah sure you can get close. Close enough to recognize the song.
My vinyl set up is better than my digital set up but both are good enough for me to enjoy the music to my satisfaction. So, lets say "close" means that I can get a pc / ipad / etc digital front end to sound 95% as good as my cary audio 303.
I do realize that this is very subjective. However, my hope is that, if I have a mac mini or ipad through a well measuring dac, that the general sound quality will be similar to what I'm used to. If that is not realistic, I would love to know what it would take to be able to stream from Tidal or the sort and have similar sound quality.
Is it because my SOTA/Alphason/Lyra Delos/Moon analogue setup is so worn and outdated? Is it because my ears are so ancient? Or is it because my Qobuz/Mytek BB streaming is so damn good?  Anyway, I'm liking digital more than analogue these days. Drum me out of the audiophile corps!  BTW, I'm very tolerant of LP noises.  As long as a tick or crunch doesn't last more than two or three revolutions I'm okay with 'em.
Get a bluesound Node used for probably $250. If you think your CD player is comparable to your TT then the Node will probably be close enough. I love mine.

So a Bluesound Node is a cut above a mac mini or Ipad as a source?

By a long way.
I think you're getting some bad advice here.  Might better try the Asylum.  A Mac Mini running Roon that sends files to something like a Senore microRendu via Ethernet with asymmetrical USB to something like an Ayre Codex DAC should serve your purpose well.  You might find the DAC on the used market.  The analog/digital bias is a matter likely to be argued throughout your lifetime.