This happened to me recently, that is, I changed my password and the sync function wouldn't work anymore until I entered my passphrase. Well it asks for a password specifically because by default when you create an Opera account, it uses your password as your passphrase unless you choose to enter a custom passphrase for your sync encryption.
Interesting enough, I changed my password in the first place because I had forgotten what my account password was When I entered my new password for sync, it kept telling me that the password was invalid even though the password to the account had been successfully changed...then it dawned on me If opera uses my password as my passphrase by default, then the password that sync is asking for wouldn't be my new password but rather my old one...the one I can't remember one
In my case I got lucky I remembered my old password, turns out that I was entering just one character of the password wrong before, so there wasn't really a reason to change password(s) in the first place
There is an up side, of sorts, if you can't remember your old password to sync your bookmarks, I discovered it before I remembered my old password. Apparently, while the Opera browser itself wont sync your bookmarks until you enter your passphrase, if you go into Android's Settings > Accounts then select your Opera account, tap on the 3dots menu, then tap Sync now, the browser will just go ahead and sync your bookmarks anyway, even without the passphrase. In the Opera browser, it will still be asking for your passphrase but if you go to Bookmarks, you'll see that your bookmarks have indeed been synced.
Please note, that the method above only works if you are using Opera's default sync encryption which uses you account password as your passphrase, which only encrypts your saved passwords. This means that if you want to sync your saved passwords that you must remember your old account password before it was changed.
If you opted to use a custom passphrase which encrypts everything then this wont work for you and you're pretty much screwed out of that Opera account. Anyway, hopefully this was help to someone