KeePassXC stores passwords in one encrypted file, a .kdbx database, on a disk you control. There is no account and no cloud. It runs on Windows, macOS, and Linux. Browser integration and TOTP codes are built in. The project is open source and is the maintained community client for the KeePass format.
The KeePassXC team does not ship a phone app. KeePassDX, Strongbox, and others can open the same file, with uneven quality. Syncing the file is your job. Syncthing works. A cloud folder works only if you remember the file is the crown jewels and the cloud can still delete it. Lose the file and the passphrase together and there is no reset email.
Use it if you want the vault to be a file. keepassxc.org
Put the KeePassXC file somewhere that syncs, then test a restore onto a second computer before you travel. Browser integration should only fill on the exact site. Disable autofill on every page if the extension offers that broader mode. TOTP inside the same file is convenient and it means one stolen database is both factors. A printed emergency sheet in a drawer is the recovery plan. There is no vendor.