I guessed at the serial number and came up with this which seems right:
https://pocketwatchdatabase.com/search/result/omega-watch-co/3381883 (looking at your new photos, I guessed right!).
I don't see any info on model/etc, so you might just have to measure it.
The numbers are sold as:
Height in MM (long ways of the cross section) x thickness in mm (short ways cross section) x total length in mm x barrel diameter (optional).
At that point, you'll need to know what sort of 'end' is on it (the bridle), this page has a picture of what they look like:
https://www.cousinsuk.com/category/mainsprings-by-list-watch-pocket
For example, see:
https://www.emmywatch.com/db/mainspring/1_7-0_11-285-9_5-man/junghans--j97/
1.70 x 0.110 x 285 x 9.5mm.
Height: You can't go any higher as it probably wont fit in the barrel then. You could possibly go slightly smaller though. Reducing height reduces overall power.
Thickness: You can go either direction a little bit, thicker is increased amplitude, thinner is reduced.
Length: This determines the total wind of the watch. Longer it is(up to a point), the longer the watch will run. Shorter will mean you h ave to wind more often.
Barrel Diameter: This one matters less?? IF you get this too high, you'll not be able to press it in off the little ring, as it'll be too large and you'll need a mainspring winder of some sort.
That said, perhaps someone who has a better idea of how to identify these will show up, you can sometimes do it by keyless works.