Everyone recommends shadowing and nobody says what it is for, what does it actually improve?

The three things you found are genuinely different and only one of them is shadowing.

Shadowing is speaking along with audio at a delay of about a second, continuously, without stopping and without a transcript in front of you. You are not repeating after, you are speaking while listening, which is what makes it hard and what makes it work.

Listen and repeat is a different exercise, and a fine one. Easier, and it trains something else.

Reading aloud along with audio is a third thing, sometimes called parallel reading. Useful, and much easier because your eyes are doing the work your ears should be doing.

What shadowing actually trains, and this is the part nobody says: it is largely a motor skill and a perception exercise, not a comprehension one. Because you have no time to think, you cannot translate, and you are forced to reproduce the rhythm, stress and connected speech of the original directly. That is why it helps pronunciation and flow specifically.

Which makes it well suited to your problem. Your listening is fine and your mouth is not - that is exactly the gap it addresses.

What it will not do is give you things to say. It builds the delivery, not the content, and people who shadow for months and still cannot hold a conversation have usually done only this.

How to do it so it works, since the failure modes are consistent.

Use audio you can almost already understand. If you are decoding meaning you cannot keep up. Slightly below your listening level, not above it.

Short clips, repeated. Thirty to sixty seconds, ten or fifteen times, rather than ten minutes once. The repetition is where the improvement is; the first pass is always bad.

No transcript on the first passes. Read it afterwards to check what you were mangling, then go back to audio only.

Stay at the delay. When you fall behind, do not stop and restart - jump back in. Stopping turns it into listen-and-repeat.

Do it out loud and at full volume. Mumbling defeats the point, since the whole exercise is training your mouth. This is why people do it while walking or driving rather than in a quiet office.

Record yourself once a week and compare against the original. Unpleasant, and it is the only way to hear the errors you cannot hear live. Your own recording from four weeks ago is the most useful feedback available to you and it costs nothing.

Ten or fifteen minutes a day is plenty. It is intense and people who try to do an hour stop within a week.

Two hours a week with an actual person did more for the slow-arrival problem in three months than a year of solo work. Not because the person teaches you anything, but because the pause is real and your brain starts optimising for it.

Shadowing on the commute, conversation twice a week. They fix different halves of what you described.

The caveat that matters for your specific complaint: shadowing will not fix the words arriving slowly.

You described two problems: pronunciation you cannot hear, and slow retrieval. Shadowing is excellent for the first and does almost nothing for the second, because in shadowing the words are handed to you. You never have to search for anything.

Retrieval improves by retrieving, which means producing language you had to find yourself:

Talk to someone, even badly, even for twenty minutes a week. Nothing substitutes for this.

Talk to yourself if there is nobody available. Narrate what you are doing, describe your day out loud. It feels ridiculous and it works, because the retrieval is real even if the listener is not.

Write, then say it. Writing gives you time to search, and the phrase you had to construct on Monday comes back faster on Thursday.

So run both: shadowing for the mouth and the ear, real output for the retrieval. They are complementary rather than alternatives, and the common mistake is doing only the one that feels productive.

One encouraging thing about your position: understanding well and speaking poorly is a normal and very recoverable stage. The material is in there; it is the retrieval path that has not been built. That is a much better problem than the reverse.