Interest Rates, Inflation, Housing: Can You Have Rising Prices (Including Tax), No Growth From Too Much Tax(es), Yet Continued Low Interest Rates?

As even the taxi drivers know, housing is hot in Canada an it is due to low interest rates.  Why are we here?  Taxi drivers know due to the economic shock of lockdowns from the covid pandemic.  

There is rampant speculation as to when interest rates will increase and Canadians, permanent residents, non-Canadians, non-residents are trying to purchase before that happens.  

Should this group be keeping its eye on inflation (as the signal for interest rate increases)? Or (fade up eerie music) keep its eye on the actual inflation from....(dum dum daaaaaaah!) TAXES! 

No doubt just to pay back this statistically significant, way out of its bounds, deficit (if we return to normal spending, nevermind mind blowing debts Canada is racking up and may have to), taxes will need to be raised.  Be aware of increases to: housing tax on multi-million dollar homes, increased provincial land (and municipal) transfer taxes on every home, increased electricty taxes for electric vehicles (you honestly do not think the government is going to let that gas station revenue stream disappear, do you?), punitive carbon taxes, wealth taxes, corporate taxes.  

As such, everything will become more expensive, effectively inflation.  If taxes makes everything more expensive, yet keep a lid on consumption and growth, then will interest rates have any association with inflation? Will interest rates' usual role as the inflation fighter continue?  If not, and interest rates remain low, will housing prices continue to rise - in a no growth, high cost of living, high tax environment?