I visited a remote file with DOS line endings over SSH, added a line and
saved. The file still has \r\n at every line, but now Emacs reports
"Unix-style LF" as the line-ending style; if I add more text and save
again, the line endings are converted to \n.

Something similar happens with remote files in iso-latin-1. After
saving, they're converted to utf-8-unix. I noticed this in `git diff`: it
reported changes in some non-ASCII text that I hadn't touched, which was
surprising.

Neither problem occurs with local files.

In GNU Emacs 29.1 (build 1, x86_64-pc-linux-gnu, GTK+ Version 3.24.31,
 cairo version 1.16.0) of 2023-07-31 built on october.example.org
Windowing system distributor 'The X.Org Foundation', version 11.0.12014000
System Description: Slackware 15.0 x86_64

Configured features:
ACL CAIRO DBUS FREETYPE GIF GLIB GMP GNUTLS GPM GSETTINGS HARFBUZZ JPEG
JSON LCMS2 LIBXML2 MODULES NOTIFY INOTIFY PDUMPER PNG RSVG SECCOMP SOUND
SQLITE3 THREADS TIFF TOOLKIT_SCROLL_BARS WEBP X11 XDBE XIM XINPUT2 XPM
GTK3 ZLIB

Important settings:
  value of $LC_COLLATE: C
  value of $LANG: en_US.UTF-8
  locale-coding-system: utf-8-unix

Major mode: Text

Minor modes in effect:
  shell-dirtrack-mode: t
  tooltip-mode: t
  global-eldoc-mode: t
  show-paren-mode: t
  electric-indent-mode: t
  mouse-wheel-mode: t
  tool-bar-mode: t
  menu-bar-mode: t
  file-name-shadow-mode: t
  global-font-lock-mode: t
  font-lock-mode: t
  blink-cursor-mode: t
  line-number-mode: t
  indent-tabs-mode: t
  transient-mark-mode: t
  auto-composition-mode: t
  auto-encryption-mode: t
  auto-compression-mode: t

Load-path shadows:
None found.

Features:
(shadow sort mail-extr emacsbug message mailcap yank-media puny dired
dired-loaddefs rfc822 mml mml-sec epa derived epg rfc6068 epg-config
gnus-util text-property-search mm-decode mm-bodies mm-encode mail-parse
rfc2231 mailabbrev gmm-utils mailheader sendmail rfc2047 rfc2045
ietf-drums mm-util mail-prsvr mail-utils mule-diag help-mode vc-hg
vc-git diff-mode easy-mmode vc-bzr vc-dispatcher tramp-cache time-stamp
tramp-sh tramp tramp-loaddefs trampver tramp-integration files-x
tramp-compat rx shell pcomplete comint ansi-osc ansi-color ring
parse-time iso8601 format-spec auth-source cl-seq eieio eieio-core
cl-macs password-cache json map byte-opt gv bytecomp byte-compile
time-date subr-x cl-loaddefs cl-lib rmc iso-transl tooltip cconv eldoc
paren electric uniquify ediff-hook vc-hooks lisp-float-type elisp-mode
mwheel term/x-win x-win term/common-win x-dnd tool-bar dnd fontset image
regexp-opt fringe tabulated-list replace newcomment text-mode lisp-mode
prog-mode register page tab-bar menu-bar rfn-eshadow isearch easymenu
timer select scroll-bar mouse jit-lock font-lock syntax font-core
term/tty-colors frame minibuffer nadvice seq simple cl-generic
indonesian philippine cham georgian utf-8-lang misc-lang vietnamese
tibetan thai tai-viet lao korean japanese eucjp-ms cp51932 hebrew greek
romanian slovak czech european ethiopic indian cyrillic chinese
composite emoji-zwj charscript charprop case-table epa-hook
jka-cmpr-hook help abbrev obarray oclosure cl-preloaded button loaddefs
theme-loaddefs faces cus-face macroexp files window text-properties
overlay sha1 md5 base64 format env code-pages mule custom widget keymap
hashtable-print-readable backquote threads dbusbind inotify lcms2
dynamic-setting system-font-setting font-render-setting cairo
move-toolbar gtk x-toolkit xinput2 x multi-tty make-network-process
emacs)

Memory information:
((conses 16 79231 16886)
 (symbols 48 9277 0)
 (strings 32 29361 2228)
 (string-bytes 1 924723)
 (vectors 16 23951)
 (vector-slots 8 1006726 172152)
 (floats 8 46 49)
 (intervals 56 356 0)
 (buffers 976 14))