Fixing an unsealed drip tray
Been there, done that.

That pan is called the secondary drip pan, and must be larger than the unit on all sides.  It should be open, and it should have either a drain that driips in an obvious place, like the center of the garage so you can be annoid by it and get it fixed.  If it has no drain, it should have an float switch that either triggers an alarm or turns the hvac unit off.

Don't tape the pan, find the leak and fix the leak.  The pan is supposed to be open.

Sometimes the air leak is where process tubing, and drain tubing exit the evaporator, and sometimes it is escaping from improperly sealed joints.

Seal the gaps around process tubing and pipes with a moldable rubbery sealant, I usually use a 3M brand that is sold as a tape with a backing that you peel off, build up the tape till it covers the gap, then press it against the bulkhead like putty,

For panel joints, use a good quality aluminum duct tape, then cover that with a coating of duct sealing mastic.  This is code in my area, everything is covered in mastic at every joint... in the trade the HVAC guys call it "pookie".  It white-ish or light grey putty that comes in tubes or tubs, and kind of looks like drywall mud...  But it isn't drywall mud, it has a rubber/latex component and is more like latex putty.  A panel joint is anywhere two panels meet, or two different object meet.  Like the joint between the two metal panels in your photos, that joint in my town would be taped and the tape covered in mastic.  The only place where you don't seal the panel is the vented cover to the furnace unit, /every/ other panel is completely sealed.  So servicing the unit requires the tech to cut the mastic, and reseal it when he is done.  The units were not designed for this, but most localities recognize that over time leaks develop in panel joints, so using tape and mastic prevents air leaks like you have right now.

I had this issue at my house.  One day I decided to service my coils, as the unit wasn't keeping up with the heat.  I expected the attic to be 140*f, but instead it was closer to 75*f...  Quite comfortable for an attic in the Texas summer.  I knew I was doing good as the attic heated up as I sealed the leaks.