I think POTUS either invited Pence to have a balance of 2:2 appearance or it could be the Dems refused to be there without him to broker the exchange.
The one thing Pence brings to the table is having been in DC before he knows how the deep state processes work, so he can help set things up the way POTUS wants and then step back and watch.
Also might be POTUS wants him there to help prep him for post ‘24 activities.
Pence also represents the “winning” vote in the Senate on ALL issues.
That’s why Trump kept talking about the votes in the Senate to Schumer: “And, if we nuke the filibuster rule, my VP will vote in my favor.”
IN YOUR FACE, Schmucky!