Yo_D1 I was under the impression that unless they have been disabled the root and admin local users should always function even when remote authentication is responding or down. This article could be related to your issue.
Saw your logged in screenshot, but didnt realize you were in single user mode. My bad! Yeah, I dont think all of the correct mounting is done at that point to support TMSH commands. As Paulius suggested, this final target link (https://my.f5.com/manage/s/article/K35811337) may be what you are after here.