Glad to hear your un-planned event did not cause you major injury.
As for the bike, it is obviously up to you. Minor damage to the Volpe's steel frame can be straightened to a trustworthy state. All the components you mentioned were damaged are most likely better off replaced. If you are unhappy with the Tiagra, the 105 gruppo is next higher offering in the Shimano hierarchy.
To fix or to buy new? I would say find a bike you would be interested in. If the repairs are, say, 80% of the price of a new bike, then go new. If less than that, fix it up. Pick your own percentage.
Some quick numbers from Performancebike.com
Shimano 105 Double crank $84
Shimano 105 Double FD $44
Shimano 105 STI Brifters $139
Cinelli Cork tape $10
Mavic MX321 $39 (not sure if it fits your bike, just picked an inexpensive mtb rim as example)
Parts total-ish $316
This does not include labor, straightening the frame, and incidentals. Performance is not typically the best price around, but you get the idea. This is assuming your rear cassette is compatible with 105 components. Again, not sure.
This is a good question to also ask in the Mechanic's forum. Those guys love to fix things.
Good luck mending.
-José
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--José
'92 Bianchi Eros
'05 Bianchi Virata
'08 Electra Straight 8 Cruiser