I have used a couple in the past. DSpace is Java based so It may be intimidating to setup. I have used this at an enterprise level and is pretty robust and stable. Years ago, I used Resource Space for my home needs, I lost interest after other priorities took over. Looking at it again seems like they still have Open Source but also commercial items as well. Hope this helps you.
Might be overkill but one of the open source asset managers like Resource Space,Tactic or Phraseanet should do it.
I second archive.org. You can contact an administrator to have a collection created just for you to upload everything to, so it's nice and organized.
If you decide to run your own, I would recommend https://www.resourcespace.com/
I handle DAM work for my company, and I'm in the middle of exploring options at the moment to replace an older system.
At the moment, the front runners are:
The system we're in the process of replacing, Razuna, relies on pretty old dependencies (some of which have not been updated in over 8 years, such as Fusebox and BlueDragon CFML Server). If you're okay with that, it's still a useful product worth looking into.
All three that I mentioned above come in open source versions that you are welcome to download and use for free (which I know can be important for non-profits with limited budgets). The two replacements that I mentioned are developed in Europe, and I believe internalization is applied to the software, with full support for Unicode and foreign languages (especially ResourceSpace, which allows you to select Arabic as the UI language).
> I want to manage the photos' folder structure independently of the DAM software
The main design principle of DAM is that you ingest content into it so other people can access it. There is little to none proper DAM products which allow you to work without injecting content into it. Especially if you want server-based solution.
If you are ready to consider DAM which requires you to injest your content into it then try ResourceSpace