Why deprecate?

Backticks are still useful for concisely expressing simple, fixed (i.e. not just expressions) commands. Using shell() where a backtick can do the job doesn't address any potentially-unexpected behavior and doesn't add clarity.

Also, backticks are not equivalent to shell():

backtick := `echo "$0" "$@"`
shell := shell('echo "$0" "$@"')

$ just --evaluate
backtick := "sh"
shell    := "echo "$0" "$@""

Mentioning shell() in this part of the README seems reasonable to me, but maybe better along the lines of "More flexible and more powerful command invocations can be achieved with the shell() function" and written at the end of the section

Nice, merged! Yah, unlike in shell scripts, backticks in just don't have any weird behaviors, so no need to deprecated them. The note is nice though.