In this post I like to inform you about and upcoming change regarding Office 365 client connectivity. Microsoft announced this already in the past and reminds admins via the Office 365 admin center about the upcoming change.
This might be subject to change anytime so please monitor your Office 365 message center to stay informed about this if it is relevant for your client infrastructure.
Based on the Office 365 ProPlus – Updates page (see link below)
Starting October 13, 2020, it will be necessary to have Office 365 ProPlus or Office perpetual in mainstream support to connect to Office 365 services.

What does this mean?
I.e. Office 2013 client connections to Office 365 (SharePoint Online, Exchange Online, OneDrive for Business …) will run out of support and won’t be supported after 13. October 2020. Office 2016/2019 connections are supported till October 2023. That’s why you should plan and migrate towards Office 365 Pro Plus/Office 2016/Office 2019 to be able keep your Office client connectivity to Microsoft Office 365.
Conclusion, opinion and summary
I recommend to plan, test and execute your Office client upgrade journey to a support Microsoft Office before the above supportability deadline in case your clients run Office 2013.