I'd guess this is less about the bicep muscle itself and more about where it connects. Bicep actually runs all the way up into the shoulder and attaches inside the shoulder joint.
When you're loading the arm in stretched backhand position off the glass, you're pulling on that tendon from the bottom. The pain shows up in the arm, but the irritated spot is up at the shoulder end.
Also, probably arm is too stiff during the hit, so all the load ends up irritating tendon ends is more pronounced.
To fix: go do doctors, offload padel and fix injury, go to gym and improve shoulder/bicep chain, ask padel coach to check and improve technique.