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In essence, yes to all of that. The aim of the EU Single Market was, and is, that consumer safety standards should be applied principally at the place of production of Union goods, so that (if you will) bad apples never leave the orchard and therefore don't require documentation, declaration or checks within the transport chain. EU producers still carry that "burden", as do UK ones to the extent that we haven't since diverged from the standards we inherited. The difference is that the EU, not recognising our post-Brexit standards regime as equivalent to theirs, require proof that GB exports conform to the latter. Sometimes, eg. for "meat", this is (and has been for decades) checked at entry to the EU as a whole (as in Ray's example above) but is more commonly checked at the place within the EU of customs clearance, supported by "trading standards" checks at the retail level.