>a new manager essentially told me that I have to move into a different role oriented towards
If you "have to", I guess you know the answer already.
The question then is "are you happy doing management stuff instead of technical stuff?"
Years ago, I accepted a management promotion (at the time, it was the only way to get more money from that company). I discovered that I hated all the budget/review/meetings stuff. I ended up keeping all the technical stuff (I never replaced myself) and just did both jobs. But that didn't really work out and I ended up moving to a new company for a tech only job. It did teach me that I didn't like management positions much and since then I only do tech work.
As far as oncall goes, the last couple companies I worked at had the official policy of "your oncall 24x7, 365". But if you work at a decent shop, there aren't that many calls to begin with and if you have decent co-workers, it is easy enough to cover each other (either officially thru rotating oncall or unofficially by telling the person calling you to call coworker X instead if you are unavailable/busy).
But I agree with previous posters - it sounds like your company is planning on outsourcing/offshoring the tech groups and will only retain the managers...