Selfhosted

i'd say start small. do the the webpage on some old hardware, maybe a wiki. content consumption things that would be uncomplicated for the group to adopt. avoid things that would mean managing accounts for other people early on. a wiki or some static page using something like modocs will be easy to run off a decent internet connection at the building. low bandwith usage and low traffic.

if your goal is to degoogle group, nextcloud could be helpful for the organisers. maybe if you have success on the simple sites you can get people on board with some hardware for a small nextcloud server. but dont plan on opening the next cloud up to the kids. thats a world of risk you don't need to open up.

As someone who has no real experience with Nextcloud: Do I 'need' it, when I already have a NAS with Synology Drive running on it, being accessible through Tailscale?

Besides the time and responsibility of running the service, your biggest cost is going to be storage and maybe even transfer. None of the cheap VPS have big storage or bandwith, so I would not offer a service like this if I were you.

Just a word of warning

Nextcloud is very finicky and can be prone to breakage. That's not the say don't use it but be realistic about the amount of work needed to maintain it.

Honestly I would just go for gsuite or office365 simply because they are less likely to break on you. It sucks that Nextcloud is a huge monolith but it is what we have.