I've been using Slack actions API and can't figure out how to use response_url to send a reply in the original message's thread.
The option with chat.postMessage doesn't really work as it requires manually adding the bot to channel.
So the answer I received from the support is:
If you want to respond in the thread, you need to set the response_type to in_channel and the thread_ts value to be the ts value sent with the interaction payload.
More information about responding to actions in thread