SharePoint sites vs. Site Collections - CONFUSED!

I think the best answer is "it depends," but this might help.How to Choose between a Team Site and a Communications Site. Yes, when you see "create site" you are actually creating a new site collection - and this is actually what you want for your collaboration spaces. You will have lots of site collections backed by Office 365 Groups for membership when you create Team Sites. (Using Create Site from SharePoint home is probably the easiest way to do this.) When you create a privae team site, you'll want to be sure to assign someone to be the Owner other than you so that they can add other members to the site, both internal and external people as needed. It looks like your questions are about a combination of "broadcast/publishing sites" and private team sites. For department sites that serve as your intranet, you now have two choices - create a "classic" site collection from the Admin center or create independent modern Communication Sites from SharePoint home. Communication Sites should not really have subsites - though they are not blocked in the UI. However, you will currently need to write some code to create a shared navigation for these independent site collections if you want to connect them to feel like a traditional intranet. If you choose to create department sites using a classic SharePoint site collection at the "root," you can create sub-sites with unique permissions for each department. Most of the time, this type of site collection has read permissions for the entire organization and unique edit/owner privileges for each department.

I'm not sure what to recommend for your Operations and Associates sites since I don't know if you are talking about collaboration spaces or communications spaces, but your Project sites should almost certainly each be modern independent site collections created from SharePoint home. That will allow you the most flexibility and security in terms of governing who can have access to each one.