Car insurance after changing vehicles

Hi everyone, I recently changed my car (from a small compact to an SUV), and my insurer recalculated my premium. The new vehicle has a much higher insurance classification, and my annual premium is increasing by almost €350. Now I’m wondering: Should I just adjust the existing contract, or is it worth switching to a completely different insurer? Does a vehicle change trigger any kind of special cancellation right, or do I have to wait until the regular cancellation deadline? Also, even if my no-claims bonus stays the same, can another insurer still be significantly cheaper? I’d really appreciate hearing about your experiences. Is switching actually worth the effort? Thanks!