What fixed the issue for me, was editing /etc/bluetooth/main.conf.
# Automatically connect both A2DP and HFP/HSP profiles for incoming
# connections. Some headsets that support both profiles will only connect the
# other one automatically so the default setting of true is usually a good
# idea.
AutoConnect=true
Next enable support for multiple profiles, which can be found a few lines below in main.conf:
# Enables Multi Profile Specification support. This allows to specify if
# system supports only Multiple Profiles Single Device (MPSD) configuration
# or both Multiple Profiles Single Device (MPSD) and Multiple Profiles Multiple
# Devices (MPMD) configurations.
# Possible values: “off”, “single”, “multiple”
MultiProfile = multiple