Dr No[Moderator Omega - Wristscan]
37505
Ref 2506 would be considered a jumbo, Kevin . . .
. . . as the case measures at 38 mm diameter. The rule of thumb is that 36 mm is the dividing line; any case diameter below that would be mid-size or small.
The reference to '30 mm' must be related to movement diameter. The family of movements that started with cal 30 introduced in '39 is casually referred to as '30 mm', but there isn't an actual model name or designation for your Omega. The same case fitted with a sub-seconds cal 265 movement would be ref 2505. Both references were issued with various dial designs and also hand variations.
If the movement hasn't been serviced since acquisition, please start searching for a local watchmaker versed in vintage. Dial, hands, and crown are all original, and should be retained. Your watchmaker may advise replacing the crown to insure water-tightness, but that would alter its appearance and diminish its appeal.
While I don't have a 2505/06, there's a contemporary ref 2272 in my collection . . .

. . . which also measures 38 mm in diameter, albeit a different case design.
Thanks for sharing both your vintage Omega and recently received extract!
Cordially,
Art