Make the interaction between `MultiProgress` and other lines below it more robust

Follow up of https://github.com/rust-lang/rustup/issues/4560.

Now we know that the last line of MultiProgress lacks a newline, and instead it adds a bunch of whitespaces so that new contents are forced to be shown on the following line.

/ # RUSTUP_TERM_PROGRESS_WHEN=always rustup check^[[J^M$
^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m|^[[0m                                                                                                                                               ^M^[[2K^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m/^[[0m                                                                                                                                               ^M^[[2K^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m/^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m|^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m/^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m/^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m/^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m-^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m-^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m-^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m-^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m\^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m\^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m\^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m\^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m|^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m|^[[0m^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m|^[[0m                                                                                                                                                 ^[[1A^M^[[2K^[[1B^M^[[2K^[[1A^[[1mstable-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[92mup to date^[[0m: 1.93.1 (01f6ddf75 2026-02-11)^M$
^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[96mChecking...^[[0m ^[[1m^[[96m|^[[0m                                                                                                                                                 ^M^[[2K^[[1mbeta-x86_64-unknown-linux-musl - ^[[0m^[[1m^[[92mup to date^[[0m: 1.94.0-beta.5 (31a40f5c8 2026-02-20)                                                                                                              ^[[1mrustup - ^[[0m^[[1m^[[33mUpdate available^[[0m : 1.29.0 -> 1.28.2^M$
/ #

https://github.com/rust-lang/rustup/issues/4560#issuecomment-3971844881

Clearly some terminal configurations are not very happy about this.

On the one hand, when the history is re-read under a different window width, the missing newline will be revealed easily.

On the other hand, in certain configs (which ones?) the line wrap is not visible at all, e.g. @epage's setup which is comprised of bash v5.3.9(1)-release inside of Zellij inside of Wezterm, running on Linux Desktop (but I wasn't able to reproduce on macOS, any DE/OS info?).

Start by reproducing RUSTUP_TERM_PROGRESS_WHEN=always rustup check with MultiProgress, focusing on the final line and subsequent shell output. Compare behavior across window widths and the Bash-in-Zellij-in-WezTerm setup described, then verify that progress output and following lines remain correctly separated without exposing terminal artifacts.