Did you try KeePassXC? It's much more actively developed and runs circles around the original KeePass:
— it's a native application (starts instantly on less powerful machines)
— can check your accounts against haveibeenpwnd.com database
— has full browser integration which works flawlessly IME
— can store SSH keys and work as an SSH agent
https://keepassxc.org/
edit: it does not support synchronization, I misremembered. Sorry.