if you want to learn, there is always lots (often too much) information available.
https://mqtt.org/ has lots of information. MQTT is a protocol for communication. It typically uses a network, which is usually Wi-Fi. I have never heard of it working over Bluetooth, but I suppose it is possible.
There are several choices for brokers. Pretty sure newer versions of HA have support for MQTT, but I always run my own broker. I currently have 3 of them running as I have made changes to my infrastructure over the years. You only need one and mine don’t talk to each other.
My reading of https://espresense.com/ says you can’t (easily) do anything other than run espresence on one esp, so it is different that esphome which lets you run multiple things on one esp (sometimes this is not a good idea).
If you want to be successful at home automation you will need to learn MANY things. If you don’t want to put in the effort to do that, there are some turnkey solutions that typically have very limited capabilities, but might cover your needs.
Based on what I read in the thread, it seems your goals are similar to running a marathon but your current skill/knowledge is not quite up to really knowing how to crawl. This means you have your work cut out for you. The learning curve is steep. You also need to ask better questions to get better help.