How many miles on donor car?
First try using donor cat or even whole exhaust. Mine is 220,000 miles and pass w/ very low numbers.
(You need to unclip Ebrake cables to get room on blue car.)
If bad etc then cat adapter use two welds for down pipe end of cat....
Small end of adapter is wrong weld to remove the cat.
you clean big end. Big end should fit new cat too. (Too late to measure.)
Carefully cut cat body enough to see the inside end of adapter.
Usually exhaust fitting are overlapping pipes even when welded. My guess flat area on down pipe is just hidden by adapter.
But don't remover adapter. If needed cut adapter at bell and use it as new flat space. Why? Clean out the weld is easy to get damage to pipe. (Grinding big weld is safer because if goes wrong then just cut adapter and use it w/ a new adapter.)