Your "reputable" sites are either less reputable than you think, or you are misunderstanding what they are saying.
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There definitely no "upgrade" from 365 to 2019 (MS no longer provides 2016, but that could be simply that the page hasn't been updated recently).
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Now, you mention non-profit organization. That is a different kettle of fish. MS will provide free or discounted copies of Office to "accredited" non-profits. You have to apply to them for recognition and a supply of licenses.
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Here is some general information from MS about getting non-profit licenses.
Non Profits
You can try to get free Non-Profit licenses:
**http://office.microsoft.com/en-us/business/microsoft-office-365-for-business-faq-FX103030232.aspx**
**http://www.microsoft.com/about/corporatecitizenship/en-us/nonprofits/whats-available/available-software/#freeSoft**
– free software available to them
There is much more info on the above link page (scroll down to the bottom of the page), here is a sample.
<snip>
**Where is Office 365 for Nonprofits available?**
Office 365 for Nonprofits will be available in up to 90 countries by July 2014. To see the full list of countries launched to date, please visit
**www.microsoft.com/office365nonprofits**. Scroll down the page and click the
Office 365 Availability by Country link.
Or you can use one of the many free or low price "Office Alternatives". They have applications that are equivalent to what you see in MS Office, but they are independently developed "copies". The names and commands may be slightly different,
but they cover most of the functionality of MS Office. Most of them can, for the most part, handle MS Office format files.
</snip>