Does the Gov have to call a session to do that?
Not anything special. Congress is charged with deciding the election contest, and also admitting its own members. It has plenary authority on those subjects. For presidential election see 3 US Code, and 3 USC 15 in particular.
Separate subject - really dynamite hearing today on Crossfire Huricane. Sen Johnson, Hawley and others interviewing Keving Brock. "Holy crap" sort of things being said. Replaying on C-SPAN2 at this moment.
Johnson has a great idea - Congress should have priority in investigating malfeasance, so that the bad actors can;t use "innvestigation iunderway" as excuse for stonewall. That is a legitimate decision by Congress. Congress has plenary authority over how courts and admin agencies operate. It can impeach and remove any of these actors, and it has the power to make ALL the rules. The only boundary is the constitution.
As far as I know, legislatures have independent power. I'd have to read GA constitution and more on GA state to get details. Governors generally have the power to call legislatures into session for issues that the Governor deems warrant doing so, but as I say a tthe start, legisltures have independent power. They just don't want to be accountable.