Improve `tarfile` streaming mode to handle very large archives

Bug report

Bug description:

I am trying to use tarfile to write very large archives, and the process is being killed by the OOM killer. I would expect+want to be able to use it in streaming mode (write an unlimited number of files) like the standard tar command line utility supports by default.

Reproduction case attached.

import gc
import io
import os
import psutil
import tarfile

if __name__ == "__main__":
    t = tarfile.open("a.tar", mode="w") # default compresslevel 9
    for i in range(1,100_000_000):
        if i % 10_000 == 0:
            gc.collect()
            process = psutil.Process(os.getpid())
            mem_info = process.memory_info()
            mem = mem_info.rss
            print(f"Iteration {i}, memory usage: {mem}")

        bs = (" "*1000 + str(i)).encode('utf8')
        with io.BytesIO(bs) as file:
            tarinfo = tarfile.TarInfo(name="cool_files/{i}.txt")
            tarinfo.size = len(bs)
            t.addfile(tarinfo, file)

The memory usage increases without bound because the list of this line in addfile():

self.members.append(tarinfo)

I'm not sure what the use-case is for this line. In write-only mode, it does not seem useful. Maybe mixed read/write? But in general it does not seem correct to assume you can fit all the tarinfo's in memory.

Edit: As a workaround, I'm setting t.members=[] manually.

CPython versions tested on:

3.13

Operating systems tested on:

Linux

Start with the tarfile implementation around TarFile.addfile() and the self.members.append(tarinfo) line, using the reported reproduction to observe memory growth. Determine the intended behavior for write-only or streaming mode, then verify that writing very large archives keeps memory bounded without breaking other tarfile use cases.