It doesn't have to be the main GPU. I'm not even sure it would be possible to pass through integrated graphics. But if all you need is HDMI output, you can use the absolute cheapest GPU you can find (assuming there's an open PCIe slot). PCIe pass-through does require CPU support (Intel VT-d or AMD-Vi) on the host and may need to be enabled in the BIOS/UEFI. I have an NVIDIA Telsa card passed through to a VM on my Proxmox server, but I'm only using it for compute; my card doesn't even have a video output.
e_t_
SMB is a network protocol developed by Microsoft. It's the protocol used by Windows computers to share files with each other. But the protocol was reverse-engineered and a program called Samba provides SMB functionality on Linux. You only see print$ because your Samba isn't configured with any file shares. You'll have to configure it. You can find guides online about how to configure Samba. Samba also maintains its own user list independent of the system. That's why your local account password didn't work.
The primary concern is switchover time. A purpose-built UPS can switch in about 10 microseconds. Those large "solar generator" battery packs switch in about 30 microseconds. That might be fast enough, but it's not guaranteed to be fast enough like a UPS is.
UPS batteries are only rated for a few years' use, so you probably are due for replacement.
Have you shopped eBay for used switches?