It is funny, because to me "only a file you have to sync (and backup)" sounds more like an advantage than setting up an entire server environment just so you can access your passwords.
{Bit,Vault}warden} both now support emergency access which will be useful if it's ever needed
Apart from that bitwarden is just wayyy easier, you simply tell the (official) app the URL to your vault and it's basically good to go. You don't have to worry about synchronization one bit. The app is also fairly nice and has all the features you need. Bitwarden also does the browser integration well, unlike keepass where it's a major pia.
Isn't the self-host server (Vaultwarden) also 3rd party?
I personally don't.
Sure I have a password manager on my phone, but it only gets a small subset of my passwords anyway. Similar any password I add on my phone is very likely to be somewhat irrelevant mostly throwaway.