Going back to the issue above, it appears to happen only with kernel series 5.15 every time my system boots up from a restart. If I previously power off my system and then I boot it up again with kernel 5.15, then I will be able to manage Bluetooth devices from Gnome Settings. This odd behaviour was introduced for me after this major update, although it never happens with kernel series 5.10.
No big deal, but still I think it’s worth reporting this in case someone else experiences the same in future releases for the other branches.
Updated inxi output below (truncated) for further reference 
System:
Kernel: 5.15.11-1-MANJARO x86_64 bits: 64 compiler: gcc v: 11.1.0
parameters: root=UUID=59c46027-8f73-4e0e-a52e-825f3df72c29 rootfstype=xfs
add_efi_memmap acpi_osi='Windows 2020' lsm=lockdown,yama,apparmor,bpf
audit=1 initrd=\initramfs-5.15-x86_64.img
Desktop: GNOME 41.2 tk: GTK 3.24.31 wm: gnome-shell dm: GDM 41.0
Distro: Manjaro Linux base: Arch Linux
Machine:
Type: Laptop System: Dell product: Inspiron 7559 v: 1.3.1
serial: <superuser required> Chassis: type: 10 serial: <superuser required>
Mobo: Dell model: 0H0CC0 v: A00 serial: <superuser required> UEFI: Dell
v: 1.3.1 date: 12/02/2018
...
Memory:
RAM: total: 15.5 GiB used: 6.86 GiB (44.3%)
RAM Report:
permissions: Unable to run dmidecode. Root privileges required.
CPU:
Info: model: Intel Core i7-6700HQ bits: 64 type: MT MCP arch: Skylake-S
family: 6 model-id: 0x5E (94) stepping: 3 microcode: 0xCC
Topology: cpus: 1x cores: 4 tpc: 2 threads: 8 smt: enabled cache:
L1: 256 KiB desc: d-4x32 KiB; i-4x32 KiB L2: 1024 KiB desc: 4x256 KiB
L3: 6 MiB desc: 1x6 MiB
Speed (MHz): avg: 2911 high: 2995 min/max: 800/3500 scaling:
driver: intel_pstate governor: powersave cores: 1: 2995 2: 2918 3: 2900
4: 2900 5: 2900 6: 2900 7: 2900 8: 2877 bogomips: 41621
...
Graphics:
Device-1: Intel HD Graphics 530 vendor: Dell driver: i915 v: kernel
bus-ID: 00:02.0 chip-ID: 8086:191b class-ID: 0300
Device-2: NVIDIA GM107M [GeForce GTX 960M] vendor: Dell driver: nouveau
v: kernel bus-ID: 02:00.0 chip-ID: 10de:139b class-ID: 0302
Device-3: Sunplus Innovation Integrated_Webcam_HD type: USB
driver: uvcvideo bus-ID: 1-4:2 chip-ID: 1bcf:28b0 class-ID: 0e02
Display: wayland server: X.org 1.21.1.2 compositor: gnome-shell driver:
loaded: modesetting,nvidia alternate: fbdev,intel,nouveau,nv,vesa
display-ID: 0 resolution: <missing: xdpyinfo>
Message: Unable to show advanced data. Required tool glxinfo missing.
Audio:
Device-1: Intel 100 Series/C230 Series Family HD Audio vendor: Dell
driver: snd_hda_intel v: kernel bus-ID: 00:1f.3 chip-ID: 8086:a170
class-ID: 0403
Sound Server-1: ALSA v: k5.15.11-1-MANJARO running: yes
Sound Server-2: JACK v: 1.9.19 running: no
Sound Server-3: PulseAudio v: 15.0 running: no
Sound Server-4: PipeWire v: 0.3.42 running: yes
...
Bluetooth:
Device-1: Intel Bluetooth wireless interface type: USB driver: btusb v: 0.8
bus-ID: 1-5:3 chip-ID: 8087:0a2a class-ID: e001
Report: rfkill ID: hci0 rfk-id: 0 state: up address: see --recommends
...
Info:
Processes: 406 Uptime: 26m wakeups: 1 Init: systemd v: 250 tool: systemctl
Compilers: gcc: 11.1.0 clang: 13.0.0 Packages: pacman: 1263 lib: 343
flatpak: 0 Shell: Zsh v: 5.8 running-in: kitty inxi: 3.3.11
EDIT: I found a very similar issue on the arch forum. Still not resolved there though.