Based on the timing, I would not immediately assume that the Samsung TV, HDMI cable, or HyperDrive has suddenly failed.
Since the setup worked normally before the macOS Sonoma 14.8.8 update, the update may have changed how the MacBook Air communicates with the external display. macOS updates can sometimes affect display detection, resolution settings, refresh rates, color settings, or HDMI communication between devices.
The pixelated or distorted image you are seeing on the TV suggests that there may be a problem with the HDMI signal, the HyperDrive adapter, or the display settings that were changed after the update. The fact that the TV now shows the desktop but not the folders that normally appear on the MacBook screen may indicate that the Mac has switched from mirroring the built-in display to using the TV as an extended display.
First, check the display settings on your MacBook Air. Open Apple menu, then System Settings, then Displays. Select the Samsung TV and check the “Use As” option. If you want the TV to show exactly what appears on the MacBook screen, choose the option to mirror the built-in display.
Apple provides instructions for managing external displays here: Apple Support: Connect a display to your Mac
You can also try forcing a simpler display setting. In the Displays settings, select a resolution of 1080p and a refresh rate of 60 Hz if those options are available. Since your Samsung TV is approximately nine years old, it may work more reliably with standard 1080p settings rather than newer display modes.
It is also worth resetting the HDMI connection completely. Shut down the MacBook Air, turn off the Samsung TV, unplug the TV from power for about one minute, disconnect the HyperDrive from the Mac, and then reconnect the HDMI cable through the HyperDrive. Turn on the TV first, select the correct HDMI input, and then start the MacBook. This can force the devices to establish a new HDMI connection.
Before purchasing a new cable or adapter, test the existing equipment if possible. Try another HDMI cable, another HDMI input on the TV, and another USB-C port on the MacBook Air. If the TV works correctly with another HDMI device, the TV itself is probably not the problem. If another display works correctly through the HyperDrive, the Samsung TV or HDMI cable becomes more suspect.
If the HyperDrive has a firmware update available, check the manufacturer support page as well. Adapter firmware updates can sometimes resolve compatibility issues after major macOS updates:
HyperDrive Support
Based on the symptoms you described, the most likely causes are a changed display configuration after the Sonoma update or an HDMI handshake problem involving the HyperDrive.
A failed TV is possible, but it is less likely because the TV displayed the Mac correctly at least once after the update.