Making claim on a system

This actually sounds like a pretty good idea, but wouldn't that mean that you'd have to start at peace with others and not cold war? If you're already at cold war why would other civs care about your claims? Unless, this is a tool for later eras, but at this point there shouldn't really be many uncolonized systems. 

Don't think it would be an bad idea to add some intel to a claimed system. Something like a information satellite.

And have a claimed system appear as a dotted circle on the map.

I have a separate idea to start relationships as Neutral not Cold war so that would address and issue:
https://www.games2gether.com/endless-space-2/ideas/160-neutral-state-for-diplomacy

But also this would be an interesting factor for peace shattering.

Currently if you are at peace and another empire colonizes a system in the middle of your empire everything is fine (of course with influence you will take it over).

But with this system if you want to be at peace you need to first settle disputes over land (star systems).

very interesting.  You come up with some great ideas.

This could also work nicely for declaring war.

If you are allied with another faction then you divide the systems before declaring war so that everyone gets a fair share of the enemy systems.

Doesn't matter which of the allied factions conquers the star system. It is automatically handed based on who was "assigned" to it when declaring war.

In this was allied war negotiations might be very interesting.