In previous issues you had mentioned adding some sort of claim cost feature, is there still plans to do this?

I never had any plans to add a claim cost feature.

Probably. I basically downgraded the priority of an API for implementing things like cost because it's possible to achieve already with bonus claims, e.g. how NumismaticClaim mod does it.
The API improvement already has an issue on the tracker though.

On the topic of bonus claims, if I were to lower a players claims, they would have more claims than their max. Is there any way for the excessive claims to either expire or be unclaimed entirely?

Were there any forge mods every created that used your api?

No, because the mod can't decide the most important claims to keep.

There is no overclaim feature correct? That goes by adjacent claims

Not sure what you mean exactly.
Just got an idea for how to deal with players that have claims over the lowered limit: #354

Did you ever add commands for adding/subtracting, or is set the only option?