The stuck "cccccccccc" repeat when the connection drops is a classic symptom: Bluetooth HID drops the "key up" signal mid-keystroke, so Windows thinks that key is still held down until you force a reconnect. That's a driver/firmware-level Bluetooth stack issue, not a hardware fault in your keyboard.
Device Manager → Bluetooth → Intel Wireless Bluetooth → Power Management tab → uncheck "Allow the computer to turn off this device to save power." This is the fix most people report actually working.
If that doesn't hold: remove and re-pair both devices fresh, and check Windows Update → Advanced options → Optional updates for a newer Surface firmware/Bluetooth driver.
If it's still unreliable: switch to a USB dongle-based keyboard/mouse instead of Bluetooth — this is a hardware-level Bluetooth stack issue, not your peripherals, so a dongle sidesteps it entirely.