Only when the lawsuit between F&P and Stardock is resolved.

So I just bought STAR CONTROL ORIGINS yesterday via client... but apparently it's not possible via browser. Any ideas, why this is so?

Maybe a bug. It's listed if you search for it on the site but it won't load the page for it. Hard to say if it's cause it's going back on sale or an unintentional site bug.

It has been back on sale for a while now. That the page is still inaccessible must be a bug.

The January 2019 update from https://www.dogarandkazon.com/ gives some news.
Essentially one of Stardock's injunction motions was denied, but the overall lawsuit debacle continues.

If it's really the end.

Back for sale on Steam. Hope to see it soon on GOG.

The court case is over. All parties signed off as dropping it and the judge signed it on Friday.
Star Control I and II also returned to sale on Steam with Stardock as the Publisher and Toys For Bob as the developer, so we may see those back here shortly too.

I highly doubt we will find out more as the settlement terms are very likely protected by an NDA.

From the court document:
"Pursuant to Rule 41(a)(1)(A)(ii) of the Federal Rules of Civil Procedure, and pursuant to a
settlement reached by and between all of the parties to the above-entitled action, Plaintiff and
Counter-Defendant Stardock Systems, Inc., Counter-Defendant Valve Corporation, CounterDefendants GOG Limited and GOG Poland Sp. z o.o., and Defendants and Counter-Claimants Paul
Reiche III and Robert Frederick Ford, through their respective counsel of record, hereby jointly
stipulate and agree that the above-entitled action, including all claims and counterclaims, shall be,
and hereby is, DISMISSED WITH PREJUDICE in its entirety. Each of the parties shall bear his
or its own attorneys’ fees and costs unless otherwise specified in the terms of the parties’ settlement
agreement and/or in other applicable agreements to which a party or the parties may be subject.
IT IS SO STIPULATED."

And as ordered by the judge:

"ORDER
Plaintiff and Counter-Defendant Stardock Systems, Inc., Counter-Defendant Valve
Corporation, Counter-Defendants GOG Limited and GOG Poland Sp. z o.o., and Defendants and
Counter-Claimants Paul Reiche III and Robert Frederick Ford, being all of the parties of record in
this action, having reached a settlement, and having stipulated by and through their respective
counsel of record, and the Court having accepted the stipulation of the parties,
IT IS HEREBY ORDERED that the above-entitled action, including all claims and
counterclaims, shall be, and hereby is, DISMISSED WITH PREJUDICE in its entirety.
IT IS FURTHER ORDERED that each of the parties shall bear his or its own attorneys’
fees and costs unless otherwise specified in the terms of the parties’ settlement agreement and/or
in other applicable agreements to which a party or the parties may be subject.
IT IS SO ORDERED.
Dated: June 7, 2019"

Okay, that sounds final; but is the court decision public that you got that information?

Yes, let me try to give half links...
courtlistener.com/docket/6239751/stardock-systems-inc-v-paul-reiche-iii/
courtlistener.com/recap/gov.uscourts.cand.320268/gov.uscourts.cand.320268.135.0.pdf
courtlistener.com/recap/gov.uscourts.cand.320268/gov.uscourts.cand.320268.136.0_1.pdf

Al right, that's all I needed to know.

I would have expected that too, but Brad Wardell claims otherwise:
https://www.reddit.com/r/starcontrol/comments/bz40uw/from_discord_none_of_settlements_terms/

So who caved to who ?

We'll see how far that really extends. I still find it unlikely either side would be disclosing financial transactions that are part of the process including such things as indemnification payments to GoG or Valve and the amounts for their legal fees if such steps were taken.

Obviously there will be some official statements concerning who now has the rights to what. Whether they will be publicly disclosing the actual signed agreement may be another thing entirely.