[PA] [CO] Will a DAC necessarily make a difference to my setup?

So I jumped in and finally got a pair the HD6XX from drop with the black friday sales. I also got the Schiit Magni 3 as an amp since it was on discount. I'm going to be using all of this as a desktop setup (next to my DT770). I did some digging and found that my motherboard has a ALC892. I'm really wondering whether a different DAC would make a big difference at all to my setup. I did some googling and reading up on the ALC892 specifically, but nothing really that helps me out all too much.

I'm also using desktop speakers (Swan M10), and I'm thinking about how I can set up everything to cleanly incorporate easy switching of using headphones/speakers without having to unplug/plug in anything, so that's a consideration for me as well. This is something I haven't really looked very deeply into, and I would greatly appreciate anybody with experience with doing something similar to point me towards a good direction with this.
So, after reading up a fair bit more on DACs in general, I have decided on a few ways I could go about this.

1. Just run the audio from my motherboard straight.
2. Buy a budget DAC like ESS Sabre ES9023
3. Go a bit more and buy something with some quality build/looks to really complete the entire setup, as well as help organize everything in a more centralized kind of set up in addition to my speakers.

I'm probably going to put off getting a DAC for now, and wait for everything to arrive and try it out before really getting into it. I really want to try some DACs to really see if I get a noticeable difference, but that seems hard since I want to test it running off my computer. For my music in recent years I've just listened to music from Spotify, and gave up the trouble of having a dedicated DAC/sourcing my own music files. So for people out there with the equipment, what are your opinions on something like the sabre (40~SGD) versus a little bit more of a "Proper" entry level like the modi 3/toppingsd30/Khadas Tone Board(1-200~ SGD), or if you even recommend using one at all.

For reference, the stuff I currently use is a DT770 Pro (80 Ohms) straight to my desktop, and my Sony XBA-N3 straight to my iphone X. My budget is up to around 150-200 SGD for now.