A smart phone or tablet (recent-ish android or ios) is required to do the initial set up the Quest 2. (The Quest 2 can't be used until that step is done)
After that, the phone/tablet isn't needed for 99% of use. The Quest can run on its own from then on. There's a few functions only in the phone app like turning developer mode on and off, but generally it's fine to not have the phone around.
For the gamer PC bit...
The Quest 2 has two modes: stand alone and link.
In stand alone mode, the Quest has its own CPU and GPU, it can run on its own. You can take the Quest out into a park and play Beat Saber (be VERY careful of sunlight though, the lenses work like magnifying glasses, even a second of direct sunlight can melt a hole in the screen). All you need is the phone for setup then the Quest 2 itself.
In Link mode, you connect the Quest 2 to a PC using either a usb cable (Link) or wifi (AirLink). You need a good VR capable PC with a Nvidia or AMD graphics card. (Weak PCs with only Intel graphics won't work at all)
In this case the Quest isn't actually running the games anymore, the PC plays the game and streams it to the headset.
Stand alone mode lets you play anywhere and don't need extra hardware. But the game library is smaller (you need Quest specific games, you can't buy them from Steam)
Link mode means you have to be close to a PC the whole time (cable or wifi range), but you have a MUCH bigger range of games (from Steam, Epic, etc). If a game has both stand alone and PC versions, the PC version (using Link) may have better graphics since the hardware is better.
Luckily you can swap between stand alone and Link at any time, so it's the best of both worlds.
You need a smart phone either way. The Quest can't connect to a PC (or do anything at all) unless you've done the smart phone setup first, it's compulsory.
Getting games actually doesn't use the phone. The Quest itself goes online using wifi to get stand alone games. The phone is used to set up your account on the headset.
(Well, you can buy games on the phone, but that just tells the quest to install them, you can do the same on the quest itself using the built in vr store)
For the HP AIO, most of them on the current HP page won't work for VR. If they only list graphics as "Intel UHD" or "Intel Iris" then they can't work. The CPUs look pretty low spec as well. Maybe the AIO dp0170z might work, it's graphics are listed as AMD Radeon Vega 8, but it's CPU is slower than the Oculus minimum requirement. The AIOs aren't intended for intense games, and VR is even more intense than normal intense games.
The requirements for connecting a Quest to a PC: https://support.oculus.com/articles/headsets-and-accessories/oculus-link/oculus-link-compatibility
I wouldn’t but the quest2. Like my self and many others it will not let you add a payment method so unless you like to only play free games or demos I would honestly save your money. Really sad to say because I really do love the quest but this problem is still very persistent and it seem like there is no fix or support in getting this corrected. Just save your money or buy a different VR headset.