Integration appears to be crashing my Bluetooth proxies and creating instabilities

[julianjwong]

I've had a wrapper around the actions to limit sending to once every 5sec but still getting issues.
I also have an automation to restart my Bluetooth proxies every hour as well as disable the UMP integration, wait 5min and reenable it. Ignore the name of my proxy, it's configured to be a pure proxy and nothing else.
The displays possibly get spammed when my door opened triggers automations in succession. E.g. front door opened, garage door opened.

Bluetooth proxy logs looks like this

Logger: homeassistant.components.esphome.manager
Source: components/esphome/manager.py:520
integration: ESPHome (documentation, issues)
First occurred: 11:25:28 AM (266211 occurrences)
Last logged: 7:11:18 PM

Bluetooth Proxy cda844: [W][bluetooth_proxy:051]: [0] [72:A8:19:ED:04:DE] Connection request ignored, state: CONNECTING
Bluetooth Proxy cda844: [W][bluetooth_proxy.connection:353]: [1] [FF:E3:A0:5B:D3:60] Error writing char/descriptor for handle 0x 6, status=133
air-quality-sensor-wp6003: [W][bluetooth_proxy:051]: [0] [72:A8:19:ED:04:DE] Connection request ignored, state: CONNECTING
Bluetooth Proxy 1e22cc: [W][bluetooth_proxy.connection:353]: [2] [FF:E3:A0:5B:D3:60] Error writing char/descriptor for handle 0x 6, status=133
air-quality-sensor-wp6003: [W][bluetooth_proxy:051]: [0] [72:A8:19:ED:04:DE] Connection request ignored, state: DISCOVERED

[julianjwong]

I also noted old scrolling messages are getting stuck on the display after the whole restart proxy and integration. Do the displays cache? This happens even after removing power to the display.
Old messages from hours prior are still somehow getting sent to and displayed on the display. Possibly caching in the Bluetooth stack?