Does Module H issue an EU-type examination certificate like module B+C?
No.
Unlike module B+C, Module H is not built around an EU-type examination certificate for a representative specimen. Under the CRA, Module H is built around approval of the manufacturer's quality system, later decisions on changes to that system, and ongoing surveillance. That is why the retained records under Part IV are the quality-system documentation, approved changes, and notified-body decisions and reports, rather than an EU-type certificate.
Annex VIII Part IV points 3.3-4.3 and 6 describe quality-system approval, change decisions, surveillance, audit reports, and retained records, not an EU-type examination certificate.
Section 5.1.6 provides the general EU product-law distinction between conformity-assessment modules, including full quality-assurance modules.