Statistics takes longer than 1.111 seconds at startup

### The problem

running debugpy reveals several remarkable timings during setup.
writing this up per request.

### What version of Home Assistant Core has the issue?

2024.2.x

### What was the last working version of Home Assistant Core?

_No response_

### What type of installation are you running?

Home Assistant OS

### Integration causing the issue

statistics

### Link to integration documentation on our website

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

### Diagnostics information

_No response_

### Example YAML snippet

_No response_

### Anything in the logs that might be useful for us?

```txt
2024-02-12 18:06:06.833 WARNING (MainThread) [asyncio] Executing result=None created at /usr/src/homeassistant/homeassistant/core.py:633> took 1.111 seconds
```

### Additional information

_No response_

Start by profiling the StatisticsSensor._initialize_from_database() entry point named in homeassistant/components/statistics/sensor.py:534, using the debugpy timing evidence in the issue. Trace the startup work that exceeds 1.111 seconds and establish a focused regression check; done means the statistics initialization no longer causes the reported startup delay.

Written by the indexing model from the issue text.