I went down this path a few years ago so I recommend you really do your research first. In short: Home theatre products are where you want to go. Forget the sound card.
I am assuming you are building a hybrid computer/hometheatre setup so I assume it is at a desk.
Short answer: No 7.1 doesn’t really exist as standalone. All in one setups are usually complete trash. PC speakers especially are bad. Yes you can find a standalone system, but I don’t recommend it.
No a soundcard can’t run a home theatre. You need a proper amplifier to run a set of speakers which a sound card can’t do. You need a few hundred watts and no hardware exists for PC to run that even if you get a 1000watt power supply. The AV receiver will have its own hardware in it that will be better than a sound card, so save your money and just get a receiver. You run the digital sound signal over HDMI to your receiver, so a sound card won’t do anything for the signal anyway.
Speaker tech doesn’t go obsolete, so I always recommend to spend well and spend once and be happy for decades with a speaker purchase.
As for AV receiver selection, it is mostly about your budget. The higher end ones $1000 or more pay licenses for all the proprietary stuff (Dolby Atmos, etc). They also have more power delivery. Mainly though, be sure to get one that is DHCP 2.2 compliant, so you don’t have issues with 4k content. A entry level $300 one should work for a computer setup, but won’t have the beef for 7.1, but will run 5.1.
Also I recommend Yamaha receivers. I have one, and the “virtual cinema front” feature does a good job of surround with my surround speakers on mydesk rather than behind me.
A proper 7.1 setup will probably cost you $5000. Yes for PC you don’t need that much power, but the cost is mainly for quality. There isn’t much point to get a cheap 7.1 setup when you can spend the same money for a better 5.1 setup, or an even better 2 or 3.1 setup.
I recommend you spend at least how much you would spend in graphics cards over 10 years. If you get a $300 card every couple of years, then spend about $1000. Remember that unlike the graphics cards, this purchase will last you decades.
You can checkout https://www.youtube.com/channel/UCF9cWy6zaWsgdAy-kv2q4VQ for guides of setting up a home theatre system and how to budget for one. For a PC you may not necessarily get tower speakers for your main channels, but ultimately the theory is the same.