[Bug]: ConciseDateFormatter doesn't handle DST changes correctly

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### Bug summary

When the time series to plot has a day light saving change and the time zone of data changes, the ticker labels formatted incorrectly. It seems to format time zone part instead of the correct base, in this example the day.

### Code for reproduction

```Python
import datetime

import matplotlib.pyplot as plt
import numpy as np

import matplotlib.dates as mdates
from zoneinfo import ZoneInfo

base = datetime.datetime(2005, 2, 1)
dates = [base + datetime.timedelta(hours=(2 * i)) for i in range(732)]
N = len(dates)
np.random.seed(19680801)
y = np.cumsum(np.random.randn(N))

fig, axs = plt.subplots(3, 1, layout='constrained', figsize=(6, 6))
lims = [(np.datetime64('2024-10-27'), np.datetime64('2024-11-10')),
(np.datetime64('2024-11-11'), np.datetime64('2024-11-22')),
(np.datetime64('2005-02-03 11:00'), np.datetime64('2005-02-04 13:20'))
]

fig, axs = plt.subplots(3, 1, layout='constrained', figsize=(6, 6))

for nn, ax in enumerate(axs):
# locator = mdates.AutoDateLocator()
locator = mdates.AutoDateLocator(tz=ZoneInfo("America/Los_Angeles"))
formatter = mdates.ConciseDateFormatter(locator)
formatter.formats = ['%y', # ticks are mostly years
'%b', # ticks are mostly months
'%d', # ticks are mostly days
'%H:%M', # hrs
'%H:%M', # min
'%S.%f', ] # secs
# these are mostly just the level above...
formatter.zero_formats = [''] + formatter.formats[:-1]
# ...except for ticks that are mostly hours, then it is nice to have
# month-day:
formatter.zero_formats[3] = '%d-%b'

formatter.offset_formats = ['',
'%Y',
'%b %Y',
'%d %b %Y',
'%d %b %Y',
'%d %b %Y %H:%M', ]
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)

ax.plot(dates, y)
ax.set_xlim(lims[nn])
axs[0].set_title('Concise Date Formatter')

plt.show()
```

### Actual outcome

### Expected outcome

2nd graph of the same image shows the expected tick labels in the graph.

### Additional information

_No response_

### Operating system

_No response_

### Matplotlib Version

3.9.2

### Matplotlib Backend

macosx

### Python version

Python 3.11.6

### Jupyter version

_No response_

### Installation

pip

Start by running the supplied Python reproduction with matplotlib.dates.AutoDateLocator and ConciseDateFormatter, focusing on the plots spanning the daylight-saving transition. Trace how ConciseDateFormatter selects date components and time-zone information for ticker labels. Done means the labels show the correct base date across DST changes while preserving the expected output in the other plots.

Written by the indexing model from the issue text.