Get a really good metal tape mearure. Measure from center of hole to the center of the other hole. It may be in inches, but is probably mm.

Just drill new holes in the drawers! They are yours, and the new pull will cover them. I would glue a chopstick or something in the old hole to keep your drill from migrating.

I would return them, and look for new ones. Most pulls, are standard between holes, so they should fit. I wouldnt want to drill more holes in my cabinets either, and my cabinets are not new ones.

Enlarge the hole. You don't need to glue anything into the existing hole, just use a jig that will guide the drill bit. Then use a washer on the backside so the screw doesn't pull through.

Don't worry about drilling more holes. They will be covered both on the front (by the new handle) and the back (by the washer).

Unfortunately I cannot find any other handles that would fit the existing holes and I don't want to drill additional holes into the drawers.

Maybe, probably one of the pulls is metric center to center hole spacing and the other is not. Determine the C-C measurement of the old existing. And look for hardware that has C-C spacing in that system of measurement. That is the only way to avoid drilling new holes.

FWIW, I don't think the new pulls look all that different enough from the old ones to be worth the trouble of replacing old w/ new.

Depending on the center to center measurement you may be able to find adjustable pulls that will work with the current holes.
Just one example:

Franklin Brass Bar Adjusta-Pull™ Cabinet Pull, Champagne Bronze, 1-3/8 in-6-5/16 in (35mm/160mm) Adjustable Drawer Handle, 5 Pack, P44365-CZ-B https://a.co/d/2wqL6lr

^^^ sorry on my phone and I don’t think the link copied correctly. Also can’t edit. Sigh.

I have to agree with ci_lantro, they really are not that much different, and wont look that much different on your cabinets. Just keep the existing ones, and avoid the hassle and expense of changing them. The old ones look like nice ones.

Ream the hole in the cabinet door/drawer larger. 2 minutes a pull and the handle covers the elongated hole. No washers needed.

Order a set of drawer stretchers from Amazon. If it were the other way around,ie screw holes in pull were less center to center than holes in drawers you would want to order a handle stretcher. Be very carful while using these tools because if you over do it drawer shrinkers and handle compressors have been on backorder since the onset of Covid.