In all likelihood, the 'modem' is a router and each apartment is on a switch port routed through the ISP's router.

A firewall-only solution will protect the devices that you have connected to the ethernet port in your apartment. Juniper, Xophos, etc.

A firewall-only solution is not typical of consumer-grade equipment. If double-NATing is not a problem, your own router is the solution.

Taping as a temporary fix will work until you can replace the cable.

I'm more concerned that it's silver. Unless the cable is tinned or shielded, I would have expected copper-colored wires.

This spray works pretty well keeping my cats away from places that I don't want them. This may also help.

I don't really understand why the server can ping things on the 10 vlan and get a response but the things on 10 can't.

This sounds like VLAN 1 is the Native VLAN, if Omada has such a thing.

A $30 surge suppressor will not prevent this from happening again. You can see the fakespot review, for what it's worth.

Even a nearby lightning strike will overcome surge protection.

As far as I know and have seen, eliminating the path for the conducted radiation is best, if not the only, way to prevent problems in the future.

A splitter will attenuated the signal. If it doesn't cause any issues, I would terminate the unused port with a 75 ohm terminator to limit the amount of reflected signal.

The bottom line, it will probably be OK.

I only meant you don't need to match vendors.

Matching vendors is not necessary. I have Ruckus APs and a Cisco 3750 switch playing nicely with pfSense and multiple VLANs, both wired and wireless.

Before going down either road, check licensing for the equipment you are considering.

The long white 'cable' is probably a tube with either a pull string for future fiber or already has the fiber in it. What does the writing say?

A splitter will attenuate signal level to/from your modem. Typically 3-7 dB, depending on the splitter. If you do not have a need to split, the coax, use a female-to-female feed-thru connector. If the signals are already marginal, don't use a splitter. Check the upstream signal level, before moving the modem. If it's getting above 42-ish dB, then splitter is a bad idea. The downstream signal level should be above -5-ish dB if you will add a splitter.

I haven't noticed the S33 getting as hot as some older modems, but I haven't paid that much attention. If it gets hot, then keep it in the open. Personally, I like to see all of the lights/LEDs.

What is the brand/model of the gateway? Is the gateway a router, modem or both?

I didn't see anything in the AT&T list for fiber. It looked like all cellular.

Be careful that the AT&T 'fiber' is fiber to the home, not fiber to somewhere near your neighborhood.

A few years ago, an AT&T salesman knocked on my door and tried to sell me fiber. There wasn't an inch of fiber in our neighborhood. I suspect it was fiber to the DSLAM and DSL to the home. It topped out at 40 Mbps.

Spectrum was cheaper and faster for the price.

See RFC 1122, section 2.3.2.1.

Is the capture filtered or is .252 down?, since I don't see .252 respond.

As u/michrech said, lag-free gaming is not possible. There will always be lag at some point. There are hundreds of posts in this subreddit about lag.

Your friend has the right idea, a dedicated WiFi6 AP wired to your router via a PoE switch. Place the AP in the same room that you will likely game wirelessly.

Do you already own the ASUS RT-AX86U Pro? If so, try it before you buy something else. 'Gaming' is mostly just marketing BS. In the consumer world 'Pro' doesn't mean much, either. The ASUS RT-AX86U looks like it will route 1 Gbps.

Whichever router you pick, disable its WiFi in favor of the 'real' AP.