Can a higher-risk deployment environment move a product into a stricter important or critical class?
Not by itself. Classification turns on core functionality against Annex III or Annex IV, not only on whether a particular customer deploys the product in a sensitive environment.
Deployment risk still matters. The Commission FAQ gives a VPN example where one VPN version intended for critical infrastructure may require stronger risk treatment than another version intended for residential use. That affects the cybersecurity risk assessment and implementation of essential requirements, but it does not by itself rewrite the Annex III or Annex IV classification.
Section 3.3 uses two VPN versions to distinguish risk treatment from important or critical classification.
Articles 7 and 8 use core functionality for classification; Article 13 ties implementation of essential requirements to risk.