Despite all my research, I couldn’t find anything that would be FOSS and operate in a generic way.
I searched for a FOSS app that could pair with Google TV over WiFi, no success.
I searched for a FOSS app that could pair with Android over bluetooth and act as a remote, no success.
I searched if there was an RS232 port on the TV, a bluetooth-to-RS232 dongle could have done the trick with some configuration, alas no RS232.
I searched if there was an HDMI-to-bluetooth dongle that could send HDMI-CEC commands, but I’m not sure that would work.
Another option, if you have an audio jack would be to use a 3.5mm IR transmitter and send “sound clips” as IR transmission. Some of these dongle are able to “read” the IR transmission and convert them into “sound”, which you can “play back” through the dongle.