Battery Advice - Omega Seamaster 120M

To be honest I know very little about watches, I have a few vintage chronographs, but I've never opened one. My daughter liked an old Omega Seamaster 120M quartz 1380 (28mm), I bought it. While it wasn't working, I thought it was likely just that it required a new battery. But when I opened the back of it, not only was the battery not seated properly, it looked like it was supposed to be seated in some sort of cradle, but that wasn't seated properly either.

After doing some Googling it was suggested that the replacement battery required was not the 364 that was in the watch; “too thin”. It suggested either a 371 (SR920SW), a 370 (SR920W), or a Renata 377 (SR626SW).

Can someone provide me with the correct battery choice?

Any chance of a photo of the movement with the battery in? Technical manual has the battery for the 1380 as being a 9911, which in non-Omega words, is a 364.
Sounds like there's a 'battery limiting spring' which I assume helps keep it in place and maybe that's missing from yours?