I can’t comment on how bots are regulated in the whole world, the laws in the whole world are outside my learning set
In the UK, there is law which is at the moment in preparation (The Online Safety Bill) that vaguely mentions bots, proposing that various legal duties should be imposed on bot creators. The thing is that so far bots have mainly been used as tools, such as directing you to certain support articles or to an advisor when it “feels” it has failed. ChatGPT is the first bot with a broader scope of skills to last - many others have come and gone in days (we remember the Microsoft bot that got discriminating and was shut down).
Current regulations that apply are merely intellectually property/licensing regulations and some others such as the Computer Misuse Act (the bot can not directly teach you how to hack or suggest any algorithms that work in this direction).
There are other directives that currently touch AI and bots, but nothing specific. There is the EU AI act which has been proposed as well