Might try a deglosser, too. Removes the sheen and softens the paint. Then, the proper primer.
You CAN put water based/borne paint over an alkyd (oil), you just have to prep it properly. All the steps. Clean, decrease, sand and/or degloss, prime… then paint. Go to a real paint store, the one you see pros at, and seek product advice.
We sometimes will replace oil painted trim rather than deal with paint adhesion issues. It is often the easier solution when doing things professionally. Hanging new doors and replacing all the trim can be a big job though. I replace lots of trim work home owners have done themselves, and their work is usually hideous. Be sure you know what you are doing before you take this on. For a proper finish you are still going to need to fill, caulk and apply a final coat in place. You cannot prepaint in the garage and just do touch ups of you want a professional look.
Sometimes a painter can source a primer that they are confident will stick. I would take a sample of the offending trim into a professional paint store and see what they have to say.
Fourthed (or is that Four-ed). I did this for a 1917 house where I removed a wall and needed matching baseboard, so I started on the pulled-up boards, removing paint (chemically, sanding, and scraping), fighting the curves and cracks, and finally gave up. I was able to duplicate the original baseboard with a design that was just 1x4, topped with a cove molding, and then an upside-down chair rail above the cove. It was a fun challenge finding replacements from a hundred years ago, and got me inspired to redo the doors, add crown molding, and do the rest of the rooms. If you’ve got a power nailer and a decent mitre box it starts going quite quickly.