it does get easier very quickly so persevere. A few tips that might help:
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hold the bars close to the stem in the centre of the bar. It makes it more stable and means very slight arm movements are much less likely to make you wobble.
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make sure you have a point in front of you to focu son - a picture or something in the distance - worst thing you can do is look down, so keep your focus ahead. DO NOT try and ride Zwift courses on your first rides where your eyes are drawn side to side or around corners
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keep a gear that requires some effort - getting your wheels spinning with some power eg SST effort, makes you more stable. You’ll probably find recovery effort levels harder than L3/L4
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the trick of starting in a door frame is a good one, or perhaps in the kitchen or garage with a work surface or bench next to you to reach for
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once you get the basics under control then spend some time doing drills moving from one side of the rollers to the other - get used to riding nearer the edge and then across the roller slowly to the other side - you’ll learn quickly how to have more overall control
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next drill is to try 1 handed spells - just lift 1 hand slightly off the bar for a few seconds and alternate. Gradually extend how long you keep it off the bars etc. Remember to keep looking straight ahead and do NOT look at the bars!
Just keep practicing and you’ll find you pretty much master it fairly quickly.