How can I privately share and collaborate on a household budget spreadsheet?

Syncthing can work if only one person edits the file at a time, but it isn’t a collaborative editor. If both copies change while disconnected, it will preserve conflicting versions rather than intelligently merge spreadsheet edits. A hosted or self-hosted web application is a better choice when either of you needs to open and modify the file independently.

A small NAS is probably the simplest private setup. Store the file there and give both of you accounts with access to it. Some NAS platforms provide remote access, and you could edit the spreadsheet with LibreOffice or a browser-based office suite. Just be aware that ordinary file sharing does not always provide safe simultaneous editing, so you should avoid opening the same file for changes at the same time unless the software supports collaboration.

A self-hosted service such as Nextcloud, possibly combined with an online office editor like Collabora or OnlyOffice, would fit this pretty well. You could run it on a home server or NAS and access the spreadsheet through a browser from either computer. It keeps the data under your control, though you’ll need to handle backups, updates, authentication, and secure remote access yourself.

There are also convenient options through Apple or Google cloud storage, and they’re much easier to maintain than a private server. If you choose one, enable strong passwords and two-factor authentication, and consider keeping an encrypted local backup. For especially sensitive financial records, a self-hosted setup or an encrypted file shared through a trusted storage provider gives you more control.