Your use doesn't count as a "word", per man bash. Tilde is only expanded to home at the start of a typically whitespace-separated word, and your tilde is in the middle of one.
> If a word begins with an unquoted tilde character (‘~’), all of the characters up to the first unquoted slash (…) are considered a tilde-prefix. (…)
> word A sequence of characters considered as a single unit by the shell. Also known as a token.
Perhaps a succinct and compliant expression could be:
export PATH="$PATH:$(printf %s ~/.local/bin)"
That comes at the cost of forking a subsell.Edit: 2.6.1 Tilde Expansion in the POSIX standard says that ~ may be expanded "following any unquoted <colon>".
https://pubs.opengroup.org/onlinepubs/9699919799/utilities/V...
That being so, the most succinct and compliant version is my first variant, with the colon moved outside the quotes:
export PATH="$PATH":~/.local/bin
Thank you for prompting me to look this up.