Nice! Maybe my favorite quartz Omega ever and a fun “midsize”/unisex model that doesn’t get the love it deserves! Hard to think of a quirkier Omega to be had for under $1500 these days.
If the bezel is seized up I would imagine it needs to be serviced, preferably by a tech with an Omega parts account. You can send it in to Omega/Swatch directly, but they will charge a lot more and take months to do it. I would advise against trying to force it yourself.
Actually, I'm not sure about that. In the USA, Omega charges $500 to service a quartz, non-chronograph, non-precious metal watch. When I looked into getting my 2561.80 serviced locally, I got three quotes ranging from $385 to $425. (My regular watchmaker doesn't work on quartz.) Since the Omega service includes a full movement replacement and a two-year warranty, the extra $115 may be reasonable.
It is true that a local watchmaker will probably be able to perform the service much quicker, depending on their backlog.
Strictly speaking these aren’t truly a quartz watch by many measures, more a mechanical-electrical hybrid like the Seiko Kinetic. As such work on them is a tad more involved than just a battery swap.
These are fun and quirky but also a bit of a pain in the ass to keep healthy. They destroy capacitors if left unused for any great length of time. Finding a healthy one is tough but keeping it healthy on a sensible budget is tougher still. As for the stuck bezel, try running some dental floss underneath and around it as that may be enough to free it up.