Very difficult question. Part of the problem is that not everything marketed as a "synth style" action is going to have the same drop weight and speed. So designations like "semi-weighted" will mean wildly different action feels from competing manufacturers. I've even encountered different actions in the same product line based on the keyboard size (you'll have synth action in the smaller keyboards and suddenly semi-weighted in the 88-key only, etc., etc., etc.).
Generally speaking, synth action are acceptable, semi-weighted preferred, and fatar are best--generally fully-weighted are considered too heavy but that's a case-by-case thing. And even that's just a baseline. Part of the problem is whether you're after they keys of a tracker organ, barker lever action (mid-19th Century), Electropneumatic action, pure electronic action, Hammond, or stage piano/synth--as each of these have a very different feel and function but are all equally "valid" types of organ manual actions that you will find in the wild. Most people are concerned with matching whatever they'll use most often professionally.
Historic types want a surprising amount of weight--so semi- and fully-weighted are closer to tracker organs, but some even say Fatar actions are the closest for tracker emulation. (It gets further tricky that while Fatar is considered a distinct keyboard type--which is fair--it doesn't mean that all Fatar keyboards function on the same internals or have the same response; albeit they're generally fairly close.) The basic idea there is that the larger the tracker organ is the heavier action will be (usually--though not always). For me, I'd go with nice wooden manual if you can find one. Tracker organs also use a form of touch sensitivity, as the speed at which the key is pressed changes the timbre and texture of the note attack envelope, which skilled tracker organ players can use to their advantage to variety to an otherwise very limited selection of stops.
Barker levers were invented for instruments so large that a tracker action would basically "freeze" such that you could probably sit on the manual and it still wouldn't open any pipes because of the intensity of the wind pressure for so many ranks of pipes was keeping the pipes closed. By putting air pressure directly into the console, the pressure could be used to help press down keys, regardless of how much wind pressure was in all or some of the instrument. When electronics were added, these became the "electropneumatic" actions, which are probably the best "average" for what a typical pipe organ action feels like. Fatar keyboards are generally considered the closest match to those, but it's quite a moving target--since no two electropneumatic actions are going to be identical, especially from different makers and different renovations. Makers like Viscount and Midiworks come closer than Fatar, but at those prices, you should generally be considering a used full console and repairing/modifying/upgrading it yourself. If the console contains no air pressure or is otherwise totally independent from the organ mechanically, then it's an electric action, which can be anything from the lightest synth touch to some wild 70mm drop weight--it just depends on what the manufacturer chose to put into the console.
For me, I just went with a set of slightly older, used M-Audio Keystations (two 61mk1 and an 88mk2) that I could get for cheap and easily stack in my (very) cramped studio space. I avoided the Keystation Pro 88 like the plague and avoided the ES line as the earlier tend to be a little better built for roughly the same amount of money. I used to own a Pro and hated it for being substantially heavier than a typical grand piano action. The first and second generation of Keystations have a "medium" semi-weighted action, and it works for me. I really like my Oxygen49 synth-style action (it was marketed as fully weighted but only the 61 and 88 in the oxygen line have fully weighted keys), which is my main keyboard when I face my screen and monitors (it's just behind my main computer keyboard and I use it for entering single-voice parts into Dorico). Despite being a synth action, it's really smooth, really responsive and feels--for lack of a better term--sophisticated--in having a weighted feel and response without having much if any weight to it. My 20-year-old Yamaha sampler with synth-style action is beyond terrible. Not having a keyboard would probably be better than that horror that was purchased at a big box store in what's starting to feel like ancient times. It served its purpose, but I definitely prefer anything else to it.
Nothing but an acoustic grand can replace or improve my Bechstein Casio GP-300, but for organ playing, it's only "fine," since I'd rather have multiple manuals with lesser quality actions than be restricted to one manual with an excellent piano keyboard. So in my space, my Oxygen controller is directly in front of me on my desk for Dorico, Cubase, generic VST experiment (especially single-voice stuff), etc.; my Keystations are on a credenza immediately to my right with a vertical monitor and no music desk (I never use physical scores for organ--they're too cumbersome as they're either drowningly large Bach anthologies that are ridiculously unwieldy or they're 4-8 page arrangements that should be taped together and put on a large music desk that I just don't have space for); and the piano (GP-300) is farther to the side on the left has a 40" tv (for scoring/spotting, composing, or looking at sheet music) that I can put a removable music stand in front of (as I do about 80% with computer and 20% with physical scores at the piano). Some day, I'll get a pedalboard, but since I'm focused more on checking fingerings or entering notation into Dorico than "proper" practicing for recital with my organ setup, etc., I can get away with not having one and preserve several vital cubit feet of equipment storage. Because, yes, I'm a maximalist and this space is crowded! If I ever get a full console or an acoustic grand, any of it will have to go elsewhere than my tiny control room...probably way-far-away elsewhere, if that.
I strongly recommend you try the keyboards you're thinking about. Buying without testing, especially if you'll use it a lot, is very risky. Most music stores, piano stores, etc. will have floor displays, and it's worth it to give those a try to help narrow your search.
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Casio GP300 & Custom organ console