I have a Pixel 10a running the latest GrapheneOS security preview release.

The device will not charge if it's unlocked when I insert the USB C cable. My device is configured with the default Charging-only when locked USB-C policy. i.e.,
Setting path: Settings > Security & privacy > Exploit protection

On insertion I see indication that charging has started, but shortly after the USB port spontaneously drops (powerBrickConnectionStatus flips to disconnected) a few seconds after a successful initial connect.

If I then unlock the device I see UsbPortSecurityHooks cycles the port (ports_disabled to ports_enabled), at which point charging resumes.

I believe the hardware is not to blame for three reasons:

The same charger and cable works fine on the same Pixel 10a when unlocked and when powered off (no GOS).
The same charger and cable works fine on a Pixel 9a and Pixel 9 Pro with OEM OS regardless of power off or power on + lock state.
The same cable was tested good using a Treedix USB Cable tester (SKU: TRX5-0816-AC).

To reproduce (Charging-only when locked)

Lock the device.
Plug in charger.
Observe: device detects charger and begins charging.
Observe: a few seconds later the charging stops while still locked.
Unlock with biometric.
Observe: device resumes charging.

I also captured a window with adb logcat for evidence. I cleaned the buffer beforehand and I inserted tags to indicate my process. The tag is UNIQUE_TAG_123ABC so they're easy to find. Below is a synopsis and snippet:

[1] Start capture

[2] Before plugging in the cable
echo "UNIQUE_TAG_123ABC insert" >> logcat.txt

[3] After observing charging start and then stop while still locked
echo "UNIQUE_TAG_123ABC stopped-locked" >> logcat.txt

[4] After unlocking with biometric and observing charging resume
echo "UNIQUE_TAG_123ABC resumed-unlocked" >> logcat.txt

Relevant excerpt (non-contiguous; noise between sections elided with <snipped>):

UNIQUE_TAG_123ABC insert
<snipped>
08:26:20.967  UsbPortManager       USB port changed: connected=true,
                                   usbDataStatus=enabled, powerBrickConnectionStatus=connected
<snipped>
08:26:25.457  UsbPortManager       USB port changed: connected=false,
                                   powerBrickConnectionStatus=disconnected,
                                   lastConnectDurationMillis=4488
08:26:25.466  UsbPortSecurityHooks keyguard is showing and there's no longer any connected
                                   USB devices, issuing the CHARGING_ONLY_IMMEDIATE command
08:26:25.466  UsbPortSecurityHooks setSecurityStateForAllPorts: charging-only_immediate
08:26:25.469  UsbPortSecurityHooks set security.deny_new_usb2 to 1
<snipped>
UNIQUE_TAG_123ABC stopped-locked
<snipped>
08:26:30.910  UsbPortSecurityHooks onKeyguardShowingStateChanged, showing false, modeSetting 2
08:26:30.910  UsbPortSecurityHooks toggling USB ports
08:26:30.910  UsbPortSecurityHooks setSecurityStateForAllPorts: ports_disabled
<snipped>
08:26:32.416  UsbPortSecurityHooks setSecurityStateForAllPorts: ports_enabled
<snipped>
08:26:32.952  UsbPortManager       USB port changed: connected=true,
                                   powerBrickConnectionStatus=connected
<snipped>
UNIQUE_TAG_123ABC resumed-unlocked

Related, Setting the policy to Charging-only always prevents charging entirely in any state while powered on.