You’re very close to the answer with Gotthard. The only reason this works is because the country is small enough to maintain political cohesion and rich enough to afford projects like this.
> their population is 6X smaller and GDP per capita is twice as high
2x per capita * 1/6 the population = 1/3 the available money
Gotthard is longer than all the tunnels in HS2 combined. Total cost: CHF 9.560 billion as of December 2015 (it opened 1 June 2016), about £6.5bn at the exchange rate at the time.
As of 2020, the budget envelope set out by the DfT is £98 billion. HS2 is not fifteen times longer than GBT, it is (currently) four.