So, I tried to search on japanese sites, first the obvious one, wikipedia. Found this:
同年後期からはスターフィッシュ・エスディのソフト販売がジョイフルテーブルとなっている。
Which tells that from 2006 the sales of Starfish SD now belongs to Joyful Table. Now, about Joyful Table, according to the same page, is owned by a board member.
The Starfish SD site is pretty much dead, as one can easily confirm:
http://www.s-f.co.jp/ (last news is from 2016)
The Joyful Table site seems to have more recent games, but also dead:
http://www.j-t.co.jp/ (latest game is from 2018)
Looking around, I found this link:
https://g-media.work/archives/company-star-fish.html
Which seems to be a description of some game devs, the one on the link is from Starfish SD. The description is almost like the guy copied from Wikipedia or old sites, the interesting part is the commentary(one of the two commentaries), which has these importants info:
「スターフィッシュ・エスデイ」の本社住所としているグランビル荻窪3階には現在、「アルパカピクチャーズ」という別会社が入っているようです。また、こちらには不動産情報をみたところ一室しかないため、ほぼ確実にこの住所には「スターフィッシュ・エスデイ」は存在しないかと思われます。
It says that the address the site was giving to Starfish SD's Headquarters is now owned by an animation studio called
Alpaca Pictures. And since there is only one room in that address, it's possible there is no Starfish SD there anymore. (The address he is commenting above is the same one you can find on japanese wikipedia page).
これは杉並区高円寺南4丁目22番2号フジビル4階に移転したためのようです。2015年の法人番号登録時点ではこちらの住所でした。「アルパカピクチャーズ」グランビル荻窪3階に入ったのも2016年のため時期的にも合致します。ただ、こちらも2019年時点ですでに引き払っているようで、現在は空室となっております。
Here he says that the dev changed their address in 2015, which agrees with Alpaca Pictures having that address since 2016. However, since 2019 the new address's room is now vacant.
ゲームの発売自体も2017年を最後に止まっており、HPの更新も同時期に停止、Facebookも2018年の更新を最後に停止しております。
The release of games stopped in 2017, the same for the website, and their Facebook page has stopped updates since 2018.
現在会社そのものが存続しているかどうかに関しては私も情報を得られませんでしたが、住所が違う点(現在住所は発見できませんでした)や、代表者が違う点、家庭用ゲーム、スマートフォンゲームの開発は現在行っていないことに関しては明記した方が情報として正しいかと思われます。
He couldn't get any information about whether or not the company is still operating, the new address is different(he couldn't find it), company's representative is different(he commented who used to be, one of them is the owner of the Joyful Table mentioned above), and thinks that it's correct to affirm that the development of games(and smartphone games) are currently not being done(it's dead, jim!)
そもそも現在も会社として活動しているのか、存続しているかも個人的には見つけられず仕舞いでした。
And to end it, he said he couldn't find anything that says if the company is even operating.
So, in another words, assume it is dead until they release something.