Hi @stephenmas I'm afraid I have no idea how to do this on Facebook. I did a quick search for it and didn't turn up anything particularly likely-looking.
You would try asking ChatGPT or Claude, they sometimes turn up results better tuned to the question you're asking.
I no longer have a Facebook account, so I can confess to not being very knowledgeable on that platform.
On Discourse (this forum) you can change your avatar to whatever you like using your preferences, but although the 'logo overlay' feature you're asking about is also possible on Discourse, we haven't enabled it for ordinary users here, as it is the IGKT's official forums - everyone would want it, rendering it nothing special.