The EU and Japan recently negotiated a Free Trade Agreement.
Will the EU and Japan therefore share a common rulebook for goods, including agrifood?
Depends on what you mean by a common rulebook, but probably not. The key points of the agreement seem to be:
Japanese tariffs on EU food imports (which are currently very high) will be reduced to zero for around 85% of goods, a saving of $1 billion or so annually
EU "Geographical Indication" protection will be respected by Japan, so e.g. only wine from the Champagne regiuon of France will be labelled as "Champagne" in Japan. Some Japanese Geographical Indicators will also be reflected in the EU.
Japanese food imports to the EU will conform to EU safety etc. requirements. (Presumably the same applies to EU food imports to Japan matching Japanese standards, but it seems the deal is primarily focussed on food moving from EU to Japan, and manufactured goods e.g. cars moving from Japan to the EU).
Japan will relax some of the technical, non-tariff barriers to EU goods being sold in Japan.
EU tariffs on Japanese cars will be removed, worth around $2 billion annually
Both sides agree to regards their data protection laws as "equivalent" allowing free flow of data between the regions.
Procurement is improved to greatly increase the ability of companies in both markets to bid on procurement contracts in the other market
There is no convergence of regulations for non-exported food, so internal Japanese rules for food production can entirely ignore EU requirements. The agreement only applies to goods moving between the two markets.
More detailed factsheet overviews can be found at the EU commission factsheets about the agreement
In any 'third-Country' trade deal that the EU does, none of its partners are required to implement EU rules in Domestic day-to-day activities; they must only be applied when the parties trade with each other. The reason why the Chequers deal referred to a 'Common' rulebook was because at the time, the UK was not really negotiating as an independent Country, but under the 'umbrella' of a certain subset of EU rules (bit like those in the Ukraine-EU deal). But Boris has now corrected this, such that the UK is indeed negotiating as a third-Country, and is therefore not subject to any EU rules in Domestic activities. Same for any other third-Country partner of the EU.