At the present time you cannot bring devices connected to an Aqara hub into your SmartThings account.
AUGUST 2022 OPTIONS
If you are willing to go through a lot of work, or if you only have one or two devices you want to bring over, you can use either IFTTT or Alexa routines (not SmartThings routines) as an intermediary and get some partial integration that way.
For this method you create a virtual device in SmartThings to act as a proxy for each Aqara device you want to see in your SmartThings app.
Now you create multiple rules in the intermediary.
For example, if this is a simple on/off switch, you create 4 rules.
A) If aqara turns the switch on, have the intermediary turn on the SmartThings virtual switch that is acting as a proxy.
B) If aqara turns the switch off, have the intermediary turn off the SmartThings virtual switch that is acting as a proxy.
C) If SmartThings turns the virtual switch on, have the intermediary turn on the Aqara switch.
D) If SmartThings turns the virtual switch off, have the intermediary turn off the Aqara switch.
As you can see, this is a lot of work to set up, but it does keep the two systems in sync. However, it may not be able to reflect all features of the device. This method works fine for a simple on/off switch, but it won’t work for a dimmer.
For devices with more complex features you may be able to use some combination of scenes and virtual devices, but it probably won’t be very satisfactory.
IFTTT options:
Alexa routines:
https://www.amazon.com/gp/help/customer/display.html?nodeId=202200080
FOR THE FUTURE: MATTER IS COMING
if you can wait about 8 months, the good news is that the home automation industry understands how frustrating this is, and a new standard, MATTER, is coming which is intended to make it much easier to use devices from different companies, even ones connected to different hubs, in the same app. All the big companies are on board with this at least partially, including Apple, Aqara, and Samsung.
So once Matter is released, now scheduled for late this fall, and each individual company has implemented its support for Matter, it should works like the following. No virtual devices, no special setup. Yay! 
The SmartThings app will be able to add the Aqara hub as a “matter bridge” and many of the aqara devices will then show up in the ST app. Pretty much the same way Aqara now works with HomeKit. From your description, this may be all you need. This will work because Aqara has announced that its platform will have two way integration with Matter. It can bring Matter devices easily into its app AND it will be able to add some of its hub models to other platforms’ apps. And this won’t change your existing Aqara/HomeKit integration, it will still work fine. 
Unfortunately, as of this writing SmartThings has only decided to go for a one way integration with Matter. It will be able to bring other companies’ Matter compliant devices into the SmartThings app. But you will NOT be able to add a SmartThings hub to another company’s app. So it still won’t show up in Apple’s HomeKit app or the Aqara app. 
Still, “half a loaf is better than none,” and it may well be that Matter will bring you everything you need, since if everything goes as planned you will then be able to easily add the Aqara hub to the SmartThings app, and many of its devices will come along with it.
But we will just have to be patient and see what actually gets delivered by the various companies over the next year or so.
Discussion thread about SmartThings and Matter:
Matter - smart home connectivity standard (formerly Project CHIP)