There’s something wrong in both schematics that i didn’t notice initially. You don’t need the 2 left most diodes since you use a center tapped transformer. The center tab of the transformer remains your ground point. your 2.8 Volt and dissipation calculations are correct. The 10uF capacitor at the input of the 7805 is a to small to have a stable voltage. I would suggest to take 1000 uF
Depending on the type of 7805 u use, if i remember well some need at least 3 volt higher as the output, which mean 8V min in… In the calculation of 6 * 1.414 i did not take into account the lost in the diodes. Probably you need a transformer with a bit higher voltage 8 - 9 volt or use a 7805 with a lower dropout… Not sure if they exist.
Depending on your mainbord you use, most use 3.3Volt but some modules require 5 Volt too. You could add a Low Dropout 3.3 Volt regulator and connect it to the 5 Volt