updater: Check if awaited instance matches current install

Also replaces any secondary usages of GetCurrentDirectory with cached
static variable.

Co-Authored-By: Richard Stanway <r1ch@r1ch.net>
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Internal Server Error - Gitea: Git with a cup of tea
500 Internal Server Error

Gitea Version: 1.28.0+dev-477-g8b6ad49a5f