Pergola problems, to fix or to demolish and build new?

Sounds like you have a big problem here. This is what I would do ASAP. How to ProceedRelieve load immediately (Temporary Shoring):If the pergola rafters are noticeably pulling the fascia outward, place temporary vertical props (such as two or three $4\times4$ or doubled $2\times4$ posts resting on solid pavers or 2-foot $2\times10$ sill blocks) under the pergola rafters near the house. Snug them into place to transfer weight to the ground and stop active tearing at the roofline.Verification: The tension pulling on the fascia is relieved, and the gap between the house and the ledger/rafters stops expanding.Detach the pergola from the house:The pergola must be completely uncoupled from the fascia board. Any surface patches or screws driven into rotted wood will continue to fail.Assess and remediate the building envelope:Once the pergola is detached, inspect behind the fascia:Rafter tails: Check if moisture wicked into the rafter ends. Soft, spongy rafter tails must be cut back and sistered with new structural framing.Fascia and soffit: Strip away all rotted fascia boards, rotted soffit plywood, and damaged drip edges.Flashing and gutters: Reinstall solid fascia backing, waterproof flashing, and gutters to restore the roof's drainage line.Re-anchor or convert the pergola:Never reattach the pergola directly to the fascia. You have two structurally sound paths:Convert to freestanding (Recommended): Add two new support posts with concrete footings on the house side. This completely decouples the pergola from the house, eliminates roof leak risk, and simplifies permitting.Engineered roof-riser brackets: If footings near the foundation are impractical, contractors use engineered standoff posts (such as SkyLift brackets) that penetrate the roof surface or soffit to bolt directly into the exterior wall's double top plate or internal rafters.