Without San Diego based Cymer they can't move forward on their latest and greatest. As far as I know they still do R&D in San Diego even after purchase.

xLight is coming up quickly... https://www.xlight.com/

"Our system produces 4X more power that enables better lithographic patterning, which is necessary to manufacture chips with smaller and more efficient feature sizes. In addition to being more powerful, our FEL system has programmable light characteristics that improve current capabilities and enable next-generation lithography (e.g., shorter wavelengths) - uniquely enabling the extension of Moore’s Law for decades. Connecting existing ASML scanners to an xLight FEL significantly improves the tool’s capabilities, delivering next-version scanner performance without the cost and complexities."

Is it supposed to work independently of other technology at some point?

Then anyways: multilateral cooperation is at the heart of scientific progress anyways. It's fitting that ASML is in a country that is culturally strongly influenced by its history of seafaring and trade. Will see how the braindrain caused by people not wanting to live their lifes in a society taht doesn't share values like these will influence that whole technological armsrace thing.

Some people in Japan are coming up with a successor to EUV as far as I remember, what was their name again?

There's Canon with nanoimprint [1] and Rapidus [2] may be working on something

[1] https://spectrum.ieee.org/nanoimprint-lithography [2] https://www.rapidus.inc/en/

Thank you, Rapidus is what I was looking for!