Question What is the right tool for gameplay animation sequencing?

I am a C# developer with a decade of experience, but I have rather limited experience in the toolset that Unity currently provides. So, I would greatly appreciate if someone told me if I understand the required workflow correctly here.

I am trying to create a game about pro wrestling. This game will have a variety of "grapple and throw" animations, for example a suplex:



The game I'm making is going to have a pretty advanced animation system, so the suplex animation in particular is going to consist of a bunch of "sub-animations":

1. The Attacker ensures that the Target is in the valid range for the suplex move. If it is - the Attacker moves around the Target to approach it from behind.
2. The Attacker grapples the Target from behind. This step is needed because there might be a variety of attacking moves that are done from this position, so I'd like to keep step 1 and 2 separate from what's happening next so that this could be reused in other types of attacks.
3. The Attacker performs the move, the Target gets thrown away, both the Attacker and the Target end up being on the ground.
4. The attacker gets back on his feet. What happens to the Target (might get up, might stay down) depends on certain conditions , and we are not that interested about it for this case.

So I'm trying to develop a system to handle all this. This system should procedurally handle transitions between these animations - e.g. for step #1 it should move the attacker to the back of the target wherever the attacker stands, so it's not as simple as making animation controller state machine.

I was thinking about making a Timeline to blend between these steps and somehow activate/deactivate script states inside the timeline. The positive side effect (if this is feasible) would be that I would actually be able to see the entire animation flow while developing each animation in the Scene window. My concern is that as far as I understand the timeline - it's made for cutscene handling so I'm thinking that could be the wrong tool for the job.

Can you please provide a hint if I'm looking at the right place? External assets that could assist with this task are also appreciated.