Libreoffice is free and open source.https://www.libreoffice.org/

https://www.collaboraoffice.com/nextcloud/ sounds like what you're looking for. I've not tried it myself as I actually like the Google docs/sheets etc offering.

If you want something online and collaborative with basic text formatting there's Etherpad (https://etherpad.org/). If however you want a full-fledged offline word-processor then there's LibreOffice Writer (https://www.libreoffice.org/).

https://cryptpad.org

@hungryphrog @nostupidquestions take a look at @nextcloud - collaborative doc editing is sort of workable on it.

If you are tech-y, Nexcloud with Libreoffice or Only Office or Colabara Office are good options. You can mess around and see what works well for you. I don't know if this is universal and happens to everyone, but immediately upon finishing my first Nextcloud server, I wiped it and did it all again with my favorite settings/options.

Just be sure to backup to a few different places in case you mess something up. Taking disk snapshots can also help you roll back any screw-ups.

Self hosted nextcloud is the way.

owncloud + collabora

Overleaf.com, but not really, because it's LaTeX

As a different, more techy, solution that can work depending on the people you collaborate with, is to use a hosted Git service for collaboration (if you want to stay completely open source, a self-hosted GitLab).

Then, change your publication workflow to write in Markdown, ReST, or one of the other ascii formats that previews correctly, and set up your CI to render the documents automatically into, e.g., pdf:s using a converter. There are all kinds of converters from Markdown/ReST -> docs, presentation, etc. formats that are as competent - if not more so - than the usual office suites. This setup offers both online editing in the GitLab instance and offline by local cloning of the Git repo.

The side effect is that this system very seriously records and preserve your document history. You can see exactly who, at what point, changed, added, and removed things. For some types of documents, this can be very important.

https://www.openoffice.org/

If you join tilde.team you will get free access to their nextcloud services

Infomaniak's office suite for kDrive uses onlyoffice and I quite like it. Plus it's encrypted.

Well there are some that offer libreoffice or only via the cloud. but that is a company offering a service. if you don't want to pay anyone anything then you can turn your pc into a nextcloud server and host libre or only office that way.