Beet edit doesn't show custom tags

Thanks for all your work on this project.

### Problem

I have a plugin that writes a custom `album_sort` tag to sort albums by year:
```
class AlbumSortPlugin(BeetsPlugin):
def __init__(self, *args, **kwargs):
album_sort_field = mediafile.MediaField(
mediafile.MP3StorageStyle(u"TSOA"),
mediafile.MP4StorageStyle(u"soal"),
mediafile.StorageStyle(u"Album Sort")
)
self.add_media_field("album_sort", album_sort_field)
self.register_listener("write", self.write)
super().__init__(*args, **kwargs)

def write(self, item, path, tags):
if tags['original_year'] == 0:
tag_year = tags['year']
else:
tag_year = tags['original_year']

if not tags.get("album_sort", None):
tags["album_sort"] = f"{tag_year} {tags['album']}"
```

This successfully writes the custom tags to my mp3s—they show up in e.g. mp3tag. However, when I run `beet edit` against the imported files, even with `-f album_sort`, they are not displayed.

I took a look at the docs, and `beet update` seemed like it would fix this, however it raised the following exception:

```sh
Traceback (most recent call last):
File "/home/me/.local/bin/beet", line 8, in
sys.exit(main())
^^^^^^
File "/home/me/.local/share/pipx/venvs/beets/lib/python3.11/site-packages/beets/ui/__init__.py", line 1865, in main
_raw_main(args)
File "/home/me/.local/share/pipx/venvs/beets/lib/python3.11/site-packages/beets/ui/__init__.py", line 1852, in _raw_main
subcommand.func(lib, suboptions, subargs)
File "/home/me/.local/share/pipx/venvs/beets/lib/python3.11/site-packages/beets/ui/commands.py", line 1742, in update_func
update_items(
File "/home/me/.local/share/pipx/venvs/beets/lib/python3.11/site-packages/beets/ui/commands.py", line 1694, in update_items
item.store(fields=item_fields)
File "/home/me/.local/share/pipx/venvs/beets/lib/python3.11/site-packages/beets/library.py", line 395, in store
super().store(fields)
File "/home/me/.local/share/pipx/venvs/beets/lib/python3.11/site-packages/beets/dbcore/db.py", line 585, in store
tx.mutate(query, subvars)
File "/home/me/.local/share/pipx/venvs/beets/lib/python3.11/site-packages/beets/dbcore/db.py", line 962, in mutate
cursor = self.db._connection().execute(statement, subvals)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
sqlite3.OperationalError: no such column: album_sort
```

This suggests the new tag was never written to `musiclibrary.db`.

n.b. `beet info` *does* show the field (perhaps because it's reading the metadata directly).

### Possible Solutions

Ideally, `musiclibrary.db` would store tags added by plugin `write` methods. If that's not possible

- Plugin modification—is there something I can change that would write the tag to sqlite/help `beet edit` find it?
- Reimporting the files does resolve the problem—this would be a workable solution if there is an import flag(s) that bypasses any modifications to metadata (not just `-A`, but also no scrub, no replaygain, no change whatsoever). Does something like this exist?

### Setup

I'm running linux, `beet --version` output:

```shell
beets version 2.0.0
Python version 3.11.9
plugins: albumsort, badfiles, bandcamp, convert, duplicates, edit, embedart, fetchart, ftintitle, info, inline, replaygain, scrub
```

Thanks!

Reproduce the issue with the plugin and inspect update_func in beets/ui/commands.py, Item.store in beets/library.py, and mutate in beets/dbcore/db.py. Trace how the custom field reaches beet edit and SQLite, then verify that existing files expose album_sort without the no-such-column failure and that the intended update behavior works.

Written by the indexing model from the issue text.