ChartBaseStyle in BarChart3D - possible bug

This appears to be an oversight in how EdgeForm[None] (the default for $\geq100$ bars) is handled when combining the different style directives for the bars¹. Essentially, EdgeForm[None] overrides any explicit EdgeForm settings, which is why they are not applied in the second case (where there are $\geq100$ bars).

To circumvent this, you can execute the following code once before plotting anything:

Charting`iBarChart3D[{}];
prot = Unprotect@Charting`iBarChart3D;
DownValues@Charting`iBarChart3D = 
  DownValues@Charting`iBarChart3D /.
   HoldPattern[
     lhs : _["ChartBaseStyle"] = cd_[
       If[cond_,
        then_,
        else_
        ],
       rest__
       ]
     ] :> (
     If[cond,
      lhs = cd[rest];
      If[! MemberQ[lhs, _EdgeForm],
       AppendTo[lhs, then]
       ],
      lhs = cd[else, rest]
      ]
     );
Protect /@ prot;

Now the second example works as expected:

BarChart3D[RandomReal[1, {10, 10}], ChartLayout -> "Grid", 
 ChartBaseStyle -> EdgeForm[{Thickness[.01], Opacity[1]}], 
 BarSpacing -> {0.7, 0.7}]

This works by modifying the way the default style for many bars in handled: Instead of simply adding EdgeForm[None] to the list of directives (which overrides any other specifications), we combine the remaining directives first. If no explicit EdgeForm directive is present, we manually append EdgeForm[] to the list.

¹The relevant code is in Charting`iBarChart3D (look for styleData["ChartBaseStyle"] = ...; handles the default styles for the bars), Charting`ConstructDirective (handles the combining of the styles) and Charting`ConstructDirectiveOrNone (handles the override of EdgeForm[None])