What's even weirder on this is that I couldn't ping the Synology from any other device, but I could go to the synology.me/remote-id link and get on to it.
Well, maybe not so weird because that is probably done by using an established outbound connection from your Synology to the Synology website. Then that connection is used to then re-connect inward when you go to the Synology website from the internet. That's going to bypass some firewall rules since the connection is already established.
The reason I asked about "does it work from the same subnet" is because you're going to bypass firewall rules, in which case you aren't hitting the "invalid" rule. So does it ping from the same subnet? If not, the invalid rule isn't causing this, it's some other problem.
Sniffer traces are last resort because it takes a lot of time to look at them. Ensure this is really what you think it is. I was assuming that this really was related to the invalid rule. If it isn't, the sniffer trace is a waste of time.
If you are trying to get to the Synology from another machine on the same subnet and disabling the "invalid" rule "fixes" the problem, then I don't understand what's going on. That wouldn't make sense.
You should become familiar with sniffer traces. Set an output file name and turn it on for 10 or 20 seconds on your WAN interface, then download it and open it in Wireshark. This is how you look at the raw traffic on your device. Knowing what you are looking at there goes a long way to building your skills.