Re: if I could swap the motherboard to a new aurora 13 and if it work or not.
you want to swap a Ryzen area 51 board to R13 case. It would not work.
But the R13 case is designed specifically for the odd shaped R13 oem board. The Ryzen board is full ATX. R13 case does not accommodate the full height ATX board.
You will lose all AlienFX light control which is done by the oem R13 board through proprietary cable. You will also lose all front IO ports which protrude through front bezel opening specifically for the odd R13 board.
A13 mobo is Dell proprietary odd shaped board which is neither ATX nor microATX.
Form factor. A standard ATX psu has no physical space to fit inside R13 case designed to house a thin small psu. If OP wants, psu would have to sit outside case.
ATX12VO is new industry standard(correct, not proprietary) but has not caught up w motherboard makers yet (only a very small number of third party board offer 12VO).
If it is a microATX board, maybe but you may need to drill custom motherboard mounting holes in R13 case. We would need measurements of R13 OEM motherboard to confirm its height is at least equal or greater than mATX board. By the look at R13, it is quite possible that a mATX board can fit in terms of vertical dimension inside chassis.
We are not even sure whether Dell OEM board follows a vestige of ATX standard of physical spacing between back IO window and PCIe slot window. I would hope they do, but if not, it becomes nearly impossible to swap a board.
You also need to figure out pinout of AlienFX led wiring so you may have a chance to hijack Dell led control and use standard RGB app to control lights.
There are 4-5 proprietary led connectors on OEM board: side lights, sys fan 1-2-3, front ambient light (integrated w power sw). This is a daunting task but I am sure some day some one curious will crack this puzzle.
And no front IO. We also need dimensions of Dell thin psu to know whether a standard SFX psu may have a chance to fit in case, or it is obligatory to have psu sit outside case.