Until I think 2013 or 2014, the border crossing on the Georgian Military Highway, which I think you are describing, was only bilaterally open (i.e. closed to non Russians / Georgians) allegedly to prevent movement of 'terrorists' across the border. Same for the Azerbaijan - Russia border.
There is no reason the 'Armenian area', aka Armenia would adopt a similar policy any time soon. However, in these times borders are subject to closures due to changes in covid infection rates.
If you have the time, Georgia is no bad place to be, even thought it's quite small, there are many weeks, if not months worth of nice travel, hiking, visiting old churches etc to fill the time. I have no idea if the Armenian border is open at the moment, but Armenia is also great, in fact I would say even more interesting than Geoegia given the long Armenian history.
If you are worried about the Turkish border closing, there is (or certainly was in 2018...) a ferry to Chornomorsk (next to Odessa) in Ukraine.
EO
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EurasiaOverland a memoir of one quarter of a million kilometres by road through all of the Former USSR, Western and Southern Asia.
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