"Move to Applications" is now always available, not just once at startup.
Previous versions asked on first launch and took "no" as final. There was no way to change your mind afterwards — the answer was stored in a file you would have no reason to know about, and the offer never came back.
Now, for as long as the app is running from somewhere other than your Applications folder, a ↑ Move to Applications button sits in the top bar. Click it whenever you like, including long after declining the first prompt.
Worth doing: automatic updates only work from the Applications folder, because that is the only place the app is allowed to replace itself.
Everything else is unchanged
The move itself was fixed in v0.15-beta, and automatic updates have worked since v0.14-beta. Downloads are still verified against their checksum, code signature, developer certificate and Apple's notarization before anything is replaced.
Verifying your download
SHA256SUMS.txt is attached to this release. To check the file you downloaded:
shasum -a 256 -c SHA256SUMS.txt