Tried the case, connection is secure there.

Tried all HDMI ports.

Has no input for power.

This adapter: https://www.amazon.com/Adapter-QGeeM-Thunderbolt-Compatible-Pixelbook/dp/B07JW7GT7H

Please get rid of the referral link. Actual link should be https://www.amazon.com/dp/B07JW7GT7H/TAS3EbWXWTSAH