This is part of the rules of ~-expansion. It is clearly stated in the Bash manual that this expansion is not performed when the ~ is quoted.

Workaround 1

Don’t quote the ~.

file=~/path/to/file

If you need to quote the rest of the filename:

file=~/"path with spaces/to/file"

(This is perfectly legal in a garden-variety shell.)

Workaround 2

Use $HOME instead of ~.

file="$HOME/path/to/file"

BTW: Shell variable types

You seem to be a little confused about the types of shell variables.

Everything is a string.

Repeat until it sinks in: Everything is a string. (Except integers, but they’re mostly hacks on top of strings AFAIK. And arrays, but they’re arrays of strings.)

This is a shell string: "foo". So is "42". So is 42. So is foo. If you don’t need to quote things, it’s reasonable not to; who wants to type "ls" "-la" "some/dir"?