I assume they're thinking about the 'offline' style where one would shuffle a database file and probably resolve conflicts. There's an app/extensions nowadays, man!
I don't even bother with a VPN, just occasionally push a 'sync' button on the roaming devices [when they return to LAN]. DB transactions [new credentials] averages ~0 per month... but there's plenty of capacity. Works extremely well.
The truth is that even with KeePassXC, I just really do not notice stale passwords across devices.
It's just really not a huge deal for me personally. Maybe it is for normal people.
I sync my databases maybe once a year if I'm lucky.
Right, that's what I was trying to emphasize. Rare syncs are totally fine here, too. I try to keep a routine but tend to slip. If not 'with my usual device' there's a tiny number of accounts I even need. They rarely change so the 'cache' is usually suitable. If not, the restriction is always short-lived.
I am not sure, whether you are trying to get at something specific, but will interpret the question in good faith:
A classical password manager reads an encrypted database. In theory, you could upload your password database (usually just one file) anywhere, and wouldn't need to worry, assuming, that you chose a sufficiently long password for decryption, and assuming, that the encryption does not have weaknesses, which would allow an attacker to decrypt it without the password. In practice, of course you still wouldn't upload your password file to a public place, to reduce risks in the future. But anyway, the idea is, that only you know the master password for the encrypted database and so no one else can read your passwords.
Apparently it has not been working without me noticing it?