Are you certain? The AnkiWeb account connected to the email address you used to post here (is that the right one?) shows history of connecting to AnkiMobile as recently as yesterday. Does the collection on that device have the decks you’re looking for?
Desktop Anki auto-syncs on open, but you can definitely cancel out of that and choose not to sync.
But my question was about where you have which versions of your collection.
If you have a collection in AnkiMobile that synced with AnkiWeb before the mis-sync today, it should already have the 20 decks that you overwrote, and you can recover your collection from there. It’s either what you see in AnkiMobile when you open the app now – or if you carried on with the mis-sync and downloaded the wrong version on that device, it will be easier to recover it there than on the server. Restoring an Automatic Backup (Recovering from Data Loss) - Anki FAQs
Let’s stay focused on recovering your collection first, but for after that – I’ll point out to you that you’re not going to be able to merge 2 separate collections via setting up syncing. That’s what it sounds like happened – you had one collection on AnkiWeb (with those 20 decks) and a separate, possibly never-been-synced, collection in desktop Anki. If you want to merge those, you should follow these steps – Syncing with AnkiWeb - Anki Manual .