Please note that the following may be wrong, because I can't currently test it since I don't have an Office 365 subscription, and because I don't have access to Office 2016.
But in general, technically there's nothing that keeps you from installing Office 2016 on any PC. If the "Install" button you are showing in your screenshot doesn't effect what you want, simply install Office 2016 from the respective installation DVD or from the respective download link that you got from your vendor. On that PC, it would be probably best to disconnect from all Office 365 / Microsoft cloud services, at least during installation. During that installation, you then will be asked to enter your product key.
Office 2016 and 2019 haven't been "integrated" into Office 365. Rather, since quite a time, the installation method for recent Office programs has been switched to "Click-To-Run" (CTR), which I personally hate. Although the installers for the different versions look similar, the 2016 CTR installer still installs 2016, the 2019 CTR installer installs 2019, and so on. I vaguely remember that you could circumvent "Click-To-Run" with Office 2016, but the process was quite complicated, including writing a XML file by hand that controls automated installation. This mechanism was for big companies that insisted on normal installation (instead of CTR) at that time.
Additionally, if you could accept choosing the license after installation (instead of during installation), you could try the following:
After installation, start one of the Office programs; let's focus on Word here. In Word, select "Account" on the side bar left in the program window. In the screen that appears, there is a button "Switch license". If you hit it, a dialog appears with a link titled "I have a product key". If you click that link, a further dialog appears where you can enter your product key. This description is for Office 2019, but the steps should be similar in Office 2016.
I could imagine that this action effects what you want, provided you're doing it in Office 2016.
As far as I know, there is no such thing as an "automatic upgrade" from 2016 to 365. Office 365 does exist in many variations, and the smallest variant still has a lot of additional features compared to the perpetual version. If it wasn't possible to operate two installations with different licenses, that would mean that Microsoft would force you to throw away a perpetual license (that you previously have bought with your hard-earned money) as soon as you have subscribed to Office 365. I'm not a fan of Microsoft, but to my best knowledge, they won't behave like that, and I doubt that it would be legal.
you will need to download a Office 2016 installerhow to do that? – Suncatcher Mar 24 '24 at 00:09I assume you don’t have the original email with the download link and/or the installation disk?nope, I bought it in 2017, which is 8 years ago, so now this message is lost. Though I remember throughout this period I installed it several times and the MS portal was providing me the separate 2016 installer. This merging of O16 with O365 was made couple of years ago, I believe – Suncatcher Mar 25 '24 at 01:13