The first function one is not particularly well-written, but harmless. The quoting of
${num}
is completely useless. Inside [[ bash does not do any word splitting after variable expansion. Double quotes never prevent variable expansion. I am not sure what the author is talking about. Shellcheck is correct to not complain. I stopped reading there.
> Double quotes never prevent variable expansion. I am not sure what the author is talking about. Shellcheck is correct to not complain. I stopped reading there.
I think it would behoove you to read the rest of the post. The double quotes are not the operative part of example there; they're only there to demonstrate that the code execution doesn't come from splatting or word splitting.
The actual code execution in Case #1 comes from the fact that bash (and other ksh descendants) run arithmetic evaluation on some strings in arithmetic contexts, regardless of their double or single quoting. That evaluation, in turn, can run arbitrary shell commands.
`-eq` is for arithmetic comparison; `=` is for string comparison. They don't do the same thing, and it's unsound to uniformly replace either with the other.
The dangerous thing here is that an undefined number of contexts exist where Bash treats strings as arithmetic expressions, which can contain arbitrary code despite not being quoted for expansion. `-eq` is just one example of that; others have linked other examples.
(This is all for case #1. With case #2, `[` and `test` are also susceptible so long as their builtin variants are used.)
Myself I typically don't script in bash. Most of the extras like [[ are not needed, you can do everything in dash. Arrays are the only feature that comes to my mind where bash would be handy.