Cheap and lithium do not go together. Have you seen what happens when lithium batteries fail?

This. I don’t know why search is impossible, or it’s unfathomable that someone else would have asked this

5 Gbps is overkill.

WiFi extenders are never the answer.

It’s not a modem. It’s an ONT or ONT/Gateway.

You need a new ISP if this is truly what is happening.

OS2. Even OM5 will be become somewhat obsolete before long. OS2 has been around for decades and is still the standard, and the most flexible.

Pretty sure you need a router, not a switch.

And throw the "ethernet splitter" in the trash - that's where it belongs.

Printers usually use mDNS for local discovery. This isn't going to work over a VPN. As others suggested, you should configure the printer with a static IP (or DHCP reservation) and then point your client/PC at that static IP.