Running two external monitors with a 2023 MacBook Pro M3 Pro

It looks to me like the clip-on laptop extender screens on either side of the MacBook Pro consumes two video signals – and counts as two screens.

A M3 Pro MacBook Pro can drive up to two external monitors using first-class hardware video output. No hub, dock, adapter, or piece of software can increase the number of first-class, hardware-supported video outputs.

Therefore, any "solution" that lets you use both "side screens" and the Samsung monitor at the same time will involve making a second-class connection to one or more of the screens, and putting up with the compromises which tend to accompany such workarounds. These may include lags, artifacts, unsuitability for any application where content changes rapidly (e.g.,, video editing, gaming), and the possibility that when Apple revises macOS, the "workaround" might break, forcing you to rely on a third-party vendor to fix things. DRM-infested streaming movie and TV services have also been known to "black out" screens when you are using workarounds.

Your basic options:

• Devices based on DisplayLink (Synaptics) or similar workaround technologies. These require installing third-party drivers on your computer. Neither these drivers alone, nor the external "stunt boxes" alone, will let you connect any displays. The drivers and the "magic decoder ring" chip sets in the "stunt boxes" work as a pair.
• Using AirPlay to stream video to something like an Apple TV set-top box or a Roku streaming stick that would then provide HDMI output for a TV or monitor. AirPlay is not as good as a hardware video connection – but I believe that you can have one AirPlay display in addition to your two hardware-supported ones. Furthermore, since AirPlay support is part of macOS, you don't need to install a driver on the Mac, or worry too much about new versions of macOS breaking AirPlay support.

Another possibility.

It looks to me as if each of those "side screens" has its own USB-C cable that leads to the MacBook Pro. That is, it appears that the screens might be totally independent except for being physically attached to one another.

You might be able to plug in just one of the "side screens", freeing up one of your hardware video outputs to let you plug in the larger Samsung curved monitor without using a workaround like DisplayLink or AirPlay. That would leave one of the side screens dark and unused, but you can't always have everything.

one other bizarre side issue:

These types of displays have been very troublesome when connected to with ONE cable to Macs with Thunderbolt-4 ports, such as those on the MacBook Pro 2023 models. Getting the display to accept power AND to accept a display signal over one cable has been an issue.

One display-maker resolved their issues with a firmware update, and some Users got relief by work-arounds including external power supplies or additional cables. Some said installing completely up-to-date MacOS fixed their issues, others said it did not.