core: AVM FRITZ!SmartHome integration no longer works on 2023.4

The problem

After my Home Assisant upgraded to 2023.4, it can no longer connect to my FRITZ!Box 7560. The integration errors out with printing the following to the protocol:

Logger: homeassistant.config_entries
Source: components/fritzbox/__init__.py:46
First occurred: 00:17:26 (2 occurrences)
Last logged: 14:19:41

    Error setting up entry fritz.box for fritzbox
    Error setting up entry FRITZ!Box 7560 (UI) for fritzbox

Traceback (most recent call last):
  File "/usr/src/homeassistant/homeassistant/config_entries.py", line 383, in async_setup
    result = await component.async_setup_entry(hass, self)
  File "/usr/src/homeassistant/homeassistant/components/fritzbox/__init__.py", line 46, in async_setup_entry
    has_templates = await hass.async_add_executor_job(fritz.has_templates)
AttributeError: 'Fritzhome' object has no attribute 'has_templates'

There have not been been any changes to the FRITZ!Box and this worked fine with 2023.3 and previous versions.

What version of Home Assistant Core has the issue?

core-2023.4.4

What was the last working version of Home Assistant Core?

core-2023.3.y

What type of installation are you running?

Home Assistant Container

Integration causing the issue

AVM FRITZ!SmartHome

Link to integration documentation on our website

https://www.home-assistant.io/integrations/fritzbox/

Diagnostics information

home-assistant_fritzbox_2023-04-14T12-31-28.037Z.log

Example YAML snippet

No response

Anything in the logs that might be useful for us?

Logger: homeassistant.config_entries
Source: components/fritzbox/__init__.py:46
First occurred: 00:17:26 (2 occurrences)
Last logged: 14:19:41

    Error setting up entry fritz.box for fritzbox
    Error setting up entry FRITZ!Box 7560 (UI) for fritzbox

Traceback (most recent call last):
  File "/usr/src/homeassistant/homeassistant/config_entries.py", line 383, in async_setup
    result = await component.async_setup_entry(hass, self)
  File "/usr/src/homeassistant/homeassistant/components/fritzbox/__init__.py", line 46, in async_setup_entry
    has_templates = await hass.async_add_executor_job(fritz.has_templates)
AttributeError: 'Fritzhome' object has no attribute 'has_templates'

Additional information

I am using a dedicated homeassistant user to connect Home Assistant with the FRITZ!Box, not the default admin account.