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Thought experiment:
1)Plug the static port.
Altimeter and VSI will never ever move again.

2)The Pitot pressure is ambient pressure + impact pressure.
If you climb then the ambient pressure goes down, but the ambient pressure
in the static system stays where it was because of #1 above air speed indicator becomes a backwards altimeter
biased by IAS.

This is exactly what happens. Been there done that.

Try to do some climbs decents and see if the Altimeter /VSI moves?

Obviously if you have an alternate static source that would be tried early on.

Pitot heat and alternate static, smash the hobbs meter.