The below is a list of Bluetooth profiles & technologies generally supported under GNU/Linux mostly via the bluetooth stack BlueZ included in mainstream distributions. As updates are frequent this may not be a complete list. However as of this writing on Sept 2019 it does include most of the technologies and Bluetooth profiles that are supported in BlueZ 5.43 and a few others that have been added since this release. For updates since BlueZ 5.43 see http://www.bluez.org/category/news/ and https://git.kernel.org/pub/scm/bluetooth/bluez.git/plain/doc/supported-f...
Additional info: OpenSuSE 15.1+, Slackware 14.2+, ZorinOS 15+, Fedora 20+, Ubuntu 17.04+, and Linux Mint 19+ include at least BlueZ 5.43 or newer and therefore have support for most, but not all the below profiles/technologies. CentOS 8+, Redhat Enterprise Linux 8+, Fedora 28+, Ubuntu 19.04+, Lubuntu 19.04+, Kubuntu 19.04+, and Mageia 7+ should for the most part (short of any bugs) support all of the below. Rolling distributions such as Parabola GNU/Linux-libre and Arch should have a recent release and will support most if not all the features below as well.
A2DP Advanced Audio Distribution Profile Supported (BlueZ) (v1.3)
AVRCP Audio/Video Remote Control Profile (Target) Supported (BlueZ) (v1.5)
AVRCS Audio/Video Remote Control Service Supported (BlueZ) (v1.5)
DI / DID / DIP Device Identification Profile / PnP Information Supported (BlueZ) (v1.3)
DUN Dial-up Networking Profile Supported (BlueZ) (v1.1)
GAVDP Generic Audio/Video Distribution Profile Supported (BlueZ) (v1.2)
GOEP Generic Object Exchange Profile Supported (BlueZ) (v2.0)
HCRP Hard Copy Cable Replacement Profile Supported (BlueZ) (v1.2)
HDP Health Device Profile Supported (BlueZ) (v1.0)
HFP Hands-Free Profile Supported (BlueZ) (v1.6)
HID Human Interface Device Profile Supported (BlueZ) (v1.1)
HSP Headset Profile / Headset Service BlueZ (BlueZ)
IAP iPod/iPhone Accessory Protocol Supported (BlueZ)
MAP Message Access Profile Supported (BlueZ) (v1.2)
MPS Multi Profile Specification Supported (BlueZ)
OBEX OBject EXchange Supported (BlueZ)
OPP Object Push Profile Supported (BlueZ) (v1.2)
PAN / PANU / PAN NAP / SYNCH Personal Area Networking Profile Supported (BlueZ) (v1.0)
PBAP / PBA / IrMC Phone Book Access Profile Supported (BlueZ) (v1.2)
SAP / SIM / rSAP SIM Access Profile / remote SIM Access Profile Supported (BlueZ)
SDS / SDP Service Directory Service / Service Discovery Profile / Service Discovery Application Profile Supported (BlueZ) (v4.2)
SPP Serial Port Profile Supported (BlueZ) (v1.1)
GAVDP (GAVDTP) Generic Audio/Video Distribution Profile Supported BlueZ (v1.2)
Health Thermometer profile (HTP) Supported BlueZ (v1.0)
Service Discovery Application Profile (SDAP) Supported (BlueZ) (v1.1)
Logical link control and adaptation protocol (L2CAP) Supported (BlueZ) (v4.2)
AVCTP A/V Control Transport Supported (BlueZ) (v1.3)
AVDTP A/V Distribution Transport Supported (BlueZ) (v1.3)
ATT Attribute Protocol Supported (BlueZ)
BNEP Bluetooth Network Encapsulation Protocol Supported (BlueZ) (v1.0)
Bluetooth Core Bluetooth Core Specifications Mostly Supported (BlueZ)
FTP File Transfer Protocol Supported (BlueZ) (v1.2)
HCRP Hardcopy Cable Replacement Profile Supported (BlueZ) (v1.2)
HIDP Human Interface Device Protocol Supported (BlueZ) (v1.1)
MCAP Multi-Channel Adaptation Protocol Supported (BlueZ) (v1.0)
RFCOMM RFCOMM Supported (BlueZ) (v1.1)
SSP Secure Simple Pairing Supported (BlueZ)
SCO Synchronous Connection-Oriented Link Supported (BlueZ)
SDP Service Discovery Protocol Supported (BlueZ) (v4.2)
SM Security Manager Protocol Probably Supported (BlueZ)
WAP Wireless Application Protocol Probably Supported (BlueZ)
ANP Alert Notification Profile Supported (BlueZ) (v1.0)
ANS Alert Notification Service Supported (BlueZ) (v1.0)
CSCP Cycling Speed and Cadence Profile Supported (BlueZ) (v1.0)
CSCS Cycling Speed and Cadence Service Supported (BlueZ) (v1.0)
DIS Device Information Service Supported (BlueZ)
GAP Generic Access Profile Supported (BlueZ) (Core Spec v4.2)
GATT Bluetooth LE Generic Attribute (GATT) Client Supported (BlueZ) (Core Spec v4.2)
HIDS HID Service Supported (BlueZ) (v1.0)
HOGP HID over GATT Profile Supported (BlueZ) (v1.0)
HRP Heart Rate Profile Supported (BlueZ) (v1.0)
HRS Heart Rate Service Supported (BlueZ) (v1.0)
PXP Proximity Profile Supported (BlueZ) (v1.0)
ScPP Scan Perameters Profile Supported (BlueZ) (v1.0)
ScPS Scan Perameters Service Supported (BlueZ) (v1.0)
TIP Time Profile Supported (BlueZ) (v1.0)