Aurora R14, will the new AMD Radeon RX 7900 XTX fit?

Dell oem gpu RTX 3900 dimensions are 267 mm long x 114 mm height x 50 mm wide.  

Dell RX 6800 XT Length: 267 mm 10.5 inches ; Width: 120 mm 4.7 inches ; Height: 50 mm 2 inches

RX 7900 XTX card's dimensions are 276 mm x 135 mm x 51 mm.

So it appears 7900 is 9 mm longer than oem gpu and 15-20 mm taller.

Likely not, but you can take measurements and compare to the card you are planning on purchasing. Not all retail cards have the same length and height, so it is important to measure before purchasing.