Debugger starts only once on Windows

Reproduce the second-debug-session failure with the tinyusb_dev_hid_composite example on Windows 11, using the Pico W and Debug Probe. Start with the OpenOCD and CMSIS-DAP output in the issue, especially the “unable to find a matching CMSIS-DAP device” error. Done means stopping and restarting the debugger works without rebooting either device.

Pico W + Debug Probe + Windows 11 + Pico Visual Studio from Pico Setup
The probe is updated to the latest firmware.
Looks like that issue is specific to tinyusb_dev_hid_composite example.
The Pico W blink example works just fine.

I can start the debugger once and it seems to work fine. Then when I stop it the probe's yellow LED stays on.
Trying to restart it gives me OpenOCD timeout:

The only way to get it to work again is to reboot both Pico W and Probe.

Logs:

Cortex-Debug: VSCode debugger extension version 1.12.1 git(652d042). Usage info: https://github.com/Marus/cortex-debug#usage
Reading symbols from arm-none-eabi-objdump --syms -C -h -w S:/Dev/GitHub/raspberrypi/pico-examples/build/usb/device/tinyusb_device_examples/hid_composite/tinyusb_dev_hid_composite.elf
Reading symbols from arm-none-eabi-nm --defined-only -S -l -C -p S:/Dev/GitHub/raspberrypi/pico-examples/build/usb/device/tinyusb_device_examples/hid_composite/tinyusb_dev_hid_composite.elf
Launching GDB: arm-none-eabi-gdb -q --interpreter=mi2
    IMPORTANT: Set "showDevDebugOutput": "raw" in "launch.json" to see verbose GDB transactions here. Very helpful to debug issues or report problems
Launching gdb-server: openocd.exe -c "gdb_port 50000" -c "tcl_port 50001" -c "telnet_port 50002" -s "S:\\Dev\\GitHub\\raspberrypi\\pico-examples" -f "c:/Users/micro/.vscode/extensions/marus25.cortex-debug-1.12.1/support/openocd-helpers.tcl" -f interface/cmsis-dap.cfg -f target/rp2040.cfg -c "adapter speed 5000"
    Please check TERMINAL tab (gdb-server) for output from openocd.exe
Finished reading symbols from objdump: Time: 56 ms
Finished reading symbols from nm: Time: 78 ms
Output radix now set to decimal 10, hex a, octal 12.
Input radix now set to decimal 10, hex a, octal 12.
Failed to launch OpenOCD GDB Server: Timeout.

Waiting for gdb server to start...[2024-06-12T19:37:52.124Z] SERVER CONSOLE DEBUG: onBackendConnect: gdb-server session connected. You can switch to "DEBUG CONSOLE" to see GDB interactions.
openocd.exe -c "gdb_port 50007" -c "tcl_port 50008" -c "telnet_port 50009" -s "S:\\Dev\\GitHub\\raspberrypi\\pico-examples" -f "c:/Users/micro/.vscode/extensions/marus25.cortex-debug-1.12.1/support/openocd-helpers.tcl" -f interface/cmsis-dap.cfg -f target/rp2040.cfg -c "adapter speed 5000"
Open On-Chip Debugger 0.12.0-g4257276 (2023-01-27-10:19)
Licensed under GNU GPL v2
For bug reports, read
        http://openocd.org/doc/doxygen/bugs.html
CDLiveWatchSetup
Info : Hardware thread awareness created
Info : Hardware thread awareness created
adapter speed: 5000 kHz

Info : Listening on port 50008 for tcl connections
Info : Listening on port 50009 for telnet connections
Error: unable to find a matching CMSIS-DAP device

[2024-06-12T19:37:52.397Z] SERVER CONSOLE DEBUG: onBackendConnect: gdb-server session closed
GDB server session ended. This terminal will be reused, waiting for next session to start...