Going back to the galaxy map after that, the system then switched to the red X "invalid system" icon.
I just checked back a couple of hours after the timer expired. It's switched back to the green "claimable" indicator. Just to check I tried to claim it. The contact let me go through the usual primary port workflow, but the confirm button only yielded a "cannot be claimed" error message. On restarting the client, it's back to "invalid system" status.
So I don't know when or if you can claim a system after the timer expires, but it's not right away.
FWIW last night I abandoned a claim on a system with the intention of reclaiming it with a more sane choice of Primary Port, and my experience so far has been identical to this.
Initially unavailable, and with the colonisation ship still present, the system changed to available again overnight but switched to unavailable / blocked as soon as I tried to complete a second claim on it this morning. The colonisation ship is gone, but the system is still showing as blocked for the account that made the original claim, and also for one of my alts based in the same location.
There were a couple of Mauve Adders this morning too, which may or may not be complicating the issue.
I'm just going to keep retrying it every few hours until it becomes available again, or someone else claims it. If it's a case of waiting for the original completion timer to expire, it'll be three weeks before it's available again. I'm hoping it's just a case of waiting for all the virtual servers to agree with each other, or at the very least for the weekly tick to occur.
In case it's relevant I had completed one delivery, 50T of something I can't even remember, to the colonisation ship prior to abandoning the claim.