tarfile silently stops/skips on bad member header (e.g. checksum mismatch)

Bug report

Bug description:

When reading a tar archive that includes a file with a bad header (such as a checksum mismatch), getmembers simply stops listing the members at that file, without reporting an error, and ignoring the files that come after it (Edit: unless ignore_zeros=True is set).

I would expect instead that getmembers lists all members, and extractfile raises a TarError when trying to extract a file with an invalid header (such as a bad chksum or typeflag).

import os
import contextlib
import subprocess
from io import BytesIO
from tarfile import TarFile, TarInfo
from tempfile import TemporaryDirectory

# generate a tar file in memory
bio = BytesIO()
with TarFile(mode="w", fileobj=bio, errorlevel=2) as tf:
    ti = TarInfo()
    ti.size = 3
    for name, data in (("foo", b"123"), ("bar", b"456"), ("quz", b"789")):
        ti.name = name
        tf.addfile(ti, BytesIO(data))

# break the checksum of the second file 'bar'
assert b"\x00006425\x00" in bio.getvalue()
broken = bio.getvalue().replace(b"\x00006425\x00", b"\x00106425\x00")

# try to read the tar file
with TarFile(fileobj=BytesIO(broken), errorlevel=2) as tf:
    for ti in tf.getmembers():
        print(repr(ti.name))
        with tf.extractfile(ti) as fh:
            print(repr(fh.read()))
# => only "foo" is extracted

with TemporaryDirectory() as td:
    with contextlib.chdir(td):
        with TarFile(fileobj=BytesIO(broken), errorlevel=2) as tf:
            tf.extractall()
        print(os.listdir())
        # => again only "foo" is extracted
        os.unlink("foo")
        with TarFile(fileobj=BytesIO(broken), errorlevel=2) as tf:
            tf.extractall(filter="data")
        print(os.listdir())
        # => filter doesn't change anything
        with open("test.tar", "wb") as fh:
            fh.write(broken)
        subprocess.run(["tar", "tvf", "test.tar"], check=False)
        # => GNU tar 1.34 correctly identifies error and continues processing

Output:

'foo'
b'123'
['foo']
['foo']
-rw-r--r-- 0/0               3 1970-01-01 00:00 foo
tar: Skipping to next header
-rw-r--r-- 0/0               3 1970-01-01 00:00 quz
tar: Exiting with failure status due to previous errors

CPython versions tested on:

3.12, 3.13

Operating systems tested on:

Linux, Windows

Reproduce the behavior with the provided BytesIO example, then start from TarFile.getmembers(), extractfile(), and extractall(), the entry points named in the report. Trace how an invalid member header is handled and how later headers are reached. Done means the bad header is reported as requested while subsequent valid members remain processable, with the affected behavior covered by tests.