Bug description

  When metadata is configured to write to sidecar only (WRITE_TO_SIDECAR_ONLY) with ExifTool:
  1. Reading GPS from the image works correctly.
  2. Writing updated GPS coordinates to the sidecar works correctly.
  3. However, when the sidecar is subsequently loaded and a different field (e.g. a tag) is modified and saved, the GPS coordinates in the sidecar revert to  the original values from the image file.

Test steps
1 Configure: read from image, write to sidecar only, ExifTool backend
2 Read and verify original GPS (59°11'8.68"N, 17°45'24.20"E)
3 Change GPS to (59°11'9.12"N, 17°46'11.45"E), verify in sidecar 
4 Add tag "Key/cat" to image/sidecar

Expected results
Sidecar has new tags and the GPS position from step 3
 
Actual results
Sidecar has new tags and bur reverted the GPS position from step 2

ADDITIONAL INFORMATION
1 exiftool version: 13.25
2 A PR that adds a new unit test gpssidecar_utest that reproduces a bug where GPS coordinatesstored in an XMP sidecar file are silently overwritten with the original image coordinates when a subsequent metadata     change (e.g. adding a tag) is applied to the sidecar.
https://invent.kde.org/kristiankarl/digikam/-/commit/d2eb63cb1745be9dfcac95bcedcb99eb500b6dec

SOFTWARE/OS VERSIONS
System:
  Host: UBUNTU-LTS-24-10 Kernel: 6.17.0-19-generic arch: x86_64 bits: 64
  Console: pty pts/3 Distro: Ubuntu 25.10 (Questing Quokka)
Machine:
  Type: Kvm System: QEMU product: Standard PC (Q35 + ICH9, 2009) v: pc-q35-9.0
    serial: <superuser required>
  Mobo: N/A model: N/A serial: N/A BIOS: SeaBIOS v: rel-1.17.0-0-gb52ca86e094d-prebuilt.qemu.org
    date: 04/01/2014
CPU:
  Info: 8x 1-core model: 13th Gen Intel Core i9-13900KF bits: 64 type: SMP cache:
    L2: 8x 4 MiB (32 MiB)
  Speed (MHz): avg: 2995 min/max: N/A cores: 1: 2995 2: 2995 3: 2995 4: 2995 5: 2995 6: 2995
    7: 2995 8: 2995
Graphics:
  Device-1: Red Hat Virtio 1.0 GPU driver: virtio-pci v: 1
  Display: server: Xwayland v: 24.1.6 driver: gpu: virtio-pci tty: 159x49 resolution: 1280x800
  API: EGL v: 1.5 drivers: kms_swrast,swrast platforms: gbm,wayland,surfaceless,device
  API: OpenGL v: 4.5 vendor: mesa v: 25.2.8-0ubuntu0.25.10.1 note: console (EGL sourced)
    renderer: llvmpipe (LLVM 20.1.8 256 bits)
  Info: Tools: api: eglinfo,glxinfo x11: xdriinfo, xdpyinfo, xprop, xrandr
Audio:
  Device-1: Intel 82801I HD Audio driver: snd_hda_intel
  API: ALSA v: k6.17.0-19-generic status: kernel-api
  Server-1: PipeWire v: 1.4.7 status: active
Network:
  Device-1: Red Hat Virtio 1.0 network driver: virtio-pci
  IF-ID-1: docker0 state: down mac: aa:fc:c2:41:75:22
  IF-ID-2: enp1s0 state: up speed: -1 duplex: unknown mac: 52:54:00:4b:ba:3c
  IF-ID-3: tun0 state: unknown speed: 10000 Mbps duplex: full mac: N/A
Drives:
  Local Storage: total: 80 GiB used: 52.04 GiB (65.1%)
  ID-1: /dev/vda model: N/A size: 80 GiB
Partition:
  ID-1: / size: 78.19 GiB used: 52.04 GiB (66.6%) fs: ext4 dev: /dev/vda2
Swap:
  ID-1: swap-1 type: file size: 8 GiB used: 0 KiB (0.0%) file: /swap.img
Sensors:
  Src: lm-sensors+/sys Message: No sensor data found using /sys/class/hwmon or lm-sensors.
Info:
  Memory: total: 32 GiB available: 30.34 GiB used: 4.2 GiB (13.8%)
  Processes: 360 Uptime: 19h 49m Init: systemd Shell: fish inxi: 3.3.39