There are two possible causes of failure for your laptop machine: device driver software, and power.
For any USB port on a computer the mobo chip that manages the port (connector socket) must he capable of performing at the standard rate for that port - in this case, of communicating at a max data transfer rate of 5 Gb/s for a standard USB 3.2 Gen1 port. Of course, the device plugged in (in your case, a SSD OR a Laptop Hard Drive unit inside the Enclosure) also must meet those requirements, and apparently they do since the system DOES work with your desktop machine. In addition, that mobo uses software called a device driver to direct exactly what the mobo chip does and how its data are interpreted by the computer into data it can use. That driver normally is supplied by the maker of the connected device (the enclosure in this case), but very often that software is widely used by many such devices so the maker of the Operating System (Windows) has included some common drivers with their OS. The maker of a device (your enclosure) may NOT supply custom driver software, and rely on what is already included with the OS. Bear in mind that the driver software included with Windows for your laptop is likely NOT the same as the driver in use in your desktop machine because the mobo components in each machine are different. So it is possible that the problem here is that the laptop machine is using driver software that does NOT suit the devcice (the enclosure) you have. In that case a different driver might ne needed. For that you might ask Tech Support at Orico if this is the case and whether they can supply a driver they believe will work.
Power is a different issue. The older USB2 ports can deliver power to a user device at 5 VDC and up to 0.5 A current. There are NO hard drives capable of running with this power limit. Old "Laptop Hard Drive" units came with special cables to allow you to connect to TWO USB2 ports simultaneously for them to work OR with their own "wall wart" power module that you MUST use to get power to the drive unit. The newer USB3 systems (now all called USB 3.2 Genn) supply power at 5 VDC again but up to 0.9 A current. The new "Laptop Hard Drive" complete units sold for use with USB3 come with only a single normal-looking cable to connect to the USB3 port, and are designed specifically with hard drive units inside that CAN work properly within that power limit although they perform at somewhat lower data transfer rates to do that. It is not common to buy such a hard drive module by itself and then install it in your own enclosure, but that can be done. Alternatively you might have obtained a hard drive unit intended for use in a laptop machine that is NOT designed for that power limit and installed that in your enclosure. So, where did that HDD unit come from? What is its power requirement spec? It is possible that your laptop computer does provide standard power at its USB3 port that is not sufficient for a drive that needs more power, whereas your desktop machine's USB3 ports can supply MORE power than the USB3 standard.
It also is possible that your laptop computer's USB3 port does NOT supply power at the normal standard USB3 max current and that is why it does not work. In that case there is a work-around although this might not suit you. For this you need to buy a POWERED USB3 HUB - one that comes with its own power supply module that you must connect to it to supply power to connected devices. You connect that to your laptop computer's USB3 port, then connect your enclosure to the Hub. In this arrangement the enclosure is supplied power by the Hub and is not limited by what the laptop's port can supply. IF that works, you know the cause and the solution.
All of this power discussion assumes a factor you have not told us. I assumed that this enclosure allows you to connect only ONE device at a time. That is, you may use it with the SSD installed, OR with the laptop hard drive installed, but never with BOTH. Is that right or not? IF this enclosure is being operated with BOTH devices installed, that increases the current required and VERY likley that requirement exceeds the USB3 standard power specs. IF that is the case, you can verify by removing one of the devices so that only ONE item is installed in the enclosure. If it works that way with your laptop computer, you know the cause of your problem. In that case you might "get away" with using the enclosure with both items installed IF you also use the powered USB3 Hub added into your system. OR, IF that enclosure comes with its own power supply module that you have NOT been using, try that.
On the other hand, IF the encolsure does contain TWO devices but removing the hard drive module leaving only the SSD installed still does NOT allow it to work with the laptop computer, then we're back to the likelihood that the laptop is using a driver that is not suited for that encolsure. An SSD only in the enclosure certainly should not exceed the 0.9 A limit.