Add current preset / custom_preset name to web server view for climate component.

**Describe the problem you have/What new integration you would like**

I'd like the climate component (specifically the thermostat in my use case, but I think this applies to the climate component in general?) show its current preset (including a custom preset that it might be in) on the esphome web server.

**Please describe your use case for this integration and alternatives you've tried:**

I'm using the preset as a way to determine if the thermostat should use a local (to the esp32) schedule or allow Home Assistant to set its schedule. It'd be great to display this information on the built-in web server in the same way that it displays the current temperature, target temperature, and mode. I think I can put something together with a text sensor but this would be much more elegant.

**Additional context**

(I really want this thermostat to be usable even if Home Assistant is completely failed so having the dashboard as functional as possible is key for me.)

Start by tracing the climate component, especially the thermostat, and the ESPHome web server view. Confirm how the current preset and custom_preset are represented, then define done as the web server showing the active preset name, including custom presets, alongside the existing climate values.

Written by the indexing model from the issue text.