Add docs for switchbot air purifier (#38966)

Co-authored-by: c0ffeeca7 <38767475+c0ffeeca7@users.noreply.github.com>

source/_integrations/switchbot.markdown

@@ -9,6 +9,7 @@ ha_category:
   - Sensor
   - Switch
   - Vacuum
+  - Fan
 ha_release: 0.78
 ha_iot_class: Local Push
 ha_codeowners:
@@ -154,6 +155,11 @@ For instructions on how to obtain the encryption key, see README in [PySwitchbot
 - [K20](https://www.switchbot.jp/products/switchbot-robot-vacuum-cleaner-k20-pro)
 - [S10](https://www.switch-bot.com/products/switchbot-floor-cleaning-robot-s10)
 
+### Air purifiers
+
+- [Air Purifier](https://www.switch-bot.com/products/switchbot-air-purifier)
+- [Air Purifier Table](https://www.switch-bot.com/products/switchbot-air-purifier-table)
+
 ## Supported functionality
 
 ### Common
@@ -432,7 +438,9 @@ Features:
 
 ### Fans
 
-Fan entities are added for Circulator Fan.
+Fan entities are added for Circulator Fan, Air Purifier, and Air Purifier Table
+
+#### Circulator Fan
 
 Features:
 
@@ -442,6 +450,26 @@ Features:
 - set mode
 - oscillate left and right
 
+#### Air Purifier
+
+This is an encrypted device.
+
+Features:
+
+- turn on
+- turn off
+- set mode
+
+#### Air Purifier Table
+
+This is an encrypted device.
+
+Features:
+
+- turn on
+- turn off
+- set mode
+
 ### Vacuums
 
 Vacuum entities are added for K10+, K10+ Pro, K10+ Pro Combo, K20, S10.