I think I may have had an issue like this in the past where the clipboard wasn’t working at all. I believe I resolved it by installing wl-clipboard. There are also a few issues related to alacritty and clipboards in their GitHub from a while back so it might be version dependent as well.
Sharing your distro may be helpful to resolving this issue.
Ok, I also run Alacritty on Arch but I’m using KDE and tmux so it might be a bit different.
Do you have save_to_clipboard = true under [selection]?