My laptop doesn’t recognize USB 3.1 C external SSD’s

The devil is in the details. "Is a USB 3 Type A-to-A cable dangerous with USB 2 ports?" The emphasis needs to be on the specifying of a USB 3 cable.

A USB 3 compliant A-to-A cable will not be dangerous if used with USB 2 ports because a USB 3 compliant A-to-A cable will have only the ground contact of the USB 2 contacts connected. The D+/D- and +5v wires are not used in a USB 3 A-to-A cable and are specified to be unconnected to avoid damage to USB 2 ports.

I suspect that the A-to-A cable used for this hub is not a compliant cable because the hub will need power to operate. Without the data wires connected the hub will be unable to be used with any USB 2 devices. It's possible the hub gets power from someplace other than the USB cable to the computer but if there's no power brick required to make the hub work then it's cable to the computer must be providing power, and that would make it a noncompliant cable.

If USB 2 devices work with the hub then that's another clue it is not compliant with the USB spec. It's possible that the USB 2 data is somehow being sent over the USB 3 data lines but this is a function that is not defined in the USB spec, there would have to then be drivers installed for whatever logic is in the hub so the computer would know to look for USB 2 devices on the USB 3 data lines.

If a USB A-to-A cable does connect the +5v contacts on both ends of the cable then using it to connect two computers will hopefully just trip a self reset circuit breaker in the port on one or both computers. In some computers this can burn out a fuse or circuit board trace in the port, which would be permanent damage but not leave the port useless as devices that are powered by means other than the port should still work. Such devices that don't rely on USB power would be something like a printer. Another outcome could be the power supply protection trips and the computer shuts down.

A worst case would be something like the USB chip controlling the port being destroyed. With many computers today having a single chip for all USB ports this means the keyboard and mouse going dead. That would likely make the computer effectively dead and worthless.

The device works well with all of my USB A ports (it comes with a very thick USB A to A cable)

That's one classic issue with the type-A port used on a USB device. Type-A ports are designated for USB hosts. You were using illegal A-A cables to connect it. Fine.

Now you are using a Type-A to Type-C cable. This cable is designed to connect USB host (type-A) to Type-C device. Therefore it has HOST SIGNATURE on CC pins in the cable's overmold. Your new Type-C is also a host, so you are attempting a host-host connection, and this fails for obvious reason.

To get your SSD enclosure to work with Type-C host, you need a Type-C to Type-A Female adapter, aka "OTG adapter.

This adapter will have DEVICE signature on Type-C end, and FEMALE Type-A port, which will act just as an ordinary PC port. Then use your illegal A-A cable.

There is no single-piece Type-C cable which will connect your illegal device with Type-C port, unless you do a serious overmold "surgery" and switch the embedded pull-up to a 5.1k pull down on one of CC pins.