Tips and tricks on how to capture Bluetooth and BLE packets.
Bluetooth and BLE PCAP file with Android
This is the easiest way to capture Bluetooth/BLE traffic if the communication only occurs between your phone and a device.
Enable Bluetooth HCI snoop log in Developper Options.

It generates a file that can directly be opened with Wireshark.
If you can start ADB as root:
adb pull /data/misc/bluetooth/logs/btsnoop_hci.log
If you can’t start ADB as root, you need to generate the bugreport archive (takes time).
adb bugreport bugreport.zip
The file is in the FS/data/misc/bluetooth/logs folder of the archive.
For BLE traffic, use the btatt Wireshark display filter.
BLE Advertisements with nRF Connect for Mobile
If you don’t need/want a full blown PCAP file and just look at BLE Advertisements payloads, nRF Connect for Mobile is a good choice.

BLE capture with nRF52840 Dongle
The Nordic Semiconductors nRF52840 Dongle can be used as sniffer for Bluetooth LE directly in Wireshark once programmed properly with nrfutil.
nrfutil install completion
nrfutil install device
nrfutil install nrf5sdk-tools
nrfutil install ble-sniffer
# Flash the dongle
nrfutil device program --serial-number FBF37Exxxxxx--firmware ~/.nrfutil/share/nrfutil-ble-sniffer/firmware/sniffer_nrf52840dongle_nrf52840_4.1.1.zip
# Wireshark stuff
# https://docs.nordicsemi.com/bundle/nrfutil/page/guides/installing_wireshark.html
mkdir -p ~/.local/lib/wireshark/extcap
nrfutil ble-sniffer bootstrap
# A capture device like /dev/ttyACM0-4.6 (nRF Sniffer for Bluetooth LE) should be present
# There is a BLE toolbar where filtering can be done
You should have a nRF Sniffer for Bluetooth LE USB device which can be used in Wireshark.
Bus 001 Device 008: ID 1915:522a Nordic Semiconductor ASA nRF Sniffer for Bluetooth LE
Negotiated speed: Full Speed (12Mbps)
Device Descriptor:
bLength 18
bDescriptorType 1
bcdUSB 2.00
bDeviceClass 0 [unknown]
bDeviceSubClass 0 [unknown]
bDeviceProtocol 0
bMaxPacketSize0 64
idVendor 0x1915 Nordic Semiconductor ASA
idProduct 0x522a nRF Sniffer for Bluetooth LE
bcdDevice 2.04
iManufacturer 1 ZEPHYR
iProduct 2 nRF Sniffer for Bluetooth LE
iSerial 3 xxxxxxxxxxxxxxxxxxx
bNumConfigurations 1

BLE capture with Python and bleak
Have a look at bletools from Matt Brown.