Well, finding details in English about Japanese laws and regulations can be pretty difficult. They do have such a page regarding FDI incentives, however the subsidies in question here are "special" and approved through a separate fund:
A sweeping budget of ¥2 trillion ($13.385 billion), spread over two years, is reserved explicitly for subsidies related to semiconductor investments.
Since these largely go to big corporations (who have plenty of personnel), there's probably not a lot of concern in making this info too easily available otherwise. Some of the articles on this mentioned that the METI negotiated the various subsidies with the companies in question.
I was also able to find out the name of one these laws enabling the special subsidies of semiconductors, batteries etc. It's the "Economic Security Promotion Act". The EU actually has more detailed page on it (in English, I mean). E.g. this what that law covers:
The guidelines set four conditions for an item to qualify for government support: it has to be essential for
the survival of the people, is currently overly reliant on external supplies, might be subject to supply
disruptions, and is needed to ensure stable supplies.
In-between, 11 goods (semiconductors, rare earths, medical supplies, fertilisers, ship parts, liquefied natural
gas, aircraft parts, cloud applications, antimicrobials, storage batteries, industrial robots and machine tools)
have been qualified as 'specifically designated important supplies'.
Businesses supplying these products will submit plans to diversify sources and stockpile goods, and can
then ask for financial support from the government.
It also spells out who is authorized to make the decisions regarding the allocation of those funds:
Major decisions are prepared and taken by the 'Council of Experts on Economic Security Legislation'
established on 25 July 2022. Members of this Expert Council have been recruited from think-tanks,
universities, business associations and big companies. The Council meets regularly, and its meetings are
steered by the Minister in charge of economic security, currently Takaishi Sanae.
Actually, I am slightly wrong about that. The 2 trillion yen for semiconductors comes from a slightly earlier program from 2021 (the New Direction of Economic and Industrial Policies, see p.8 here), and is under the authority of METI, not of the new ministry.