If your hands shake while recording, the first step is technically improving your grip when you're filming. Hold your phone with both hands, rest your elbows against your body or a surface, or try to move as little as possible. Your Galaxy A55's optical stabilization already works pretty well, so software might actually be enough without spending money.
CapCut does stabilize quite a bit in post-production, but there's a detail people underestimate: if you use stabilization at values that are too high, the video looks weird, like it's "stuck" on the screen, with smooth but unnatural movements. Try starting with a medium value (like 50-60%) and only increase it if you really need to. The important thing is that stabilization works better on video with slow pans rather than frantic shaking, so if you can, avoid sudden movements while recording.
If CapCut still doesn't satisfy you after testing it properly, then yeah, a budget stabilizer (like a three-axis gimbal for smartphones, starting from €30-50) would make a difference. But test it to the max in post first: lots of vlog creators don't use anything fancy, software usually does the job.